V.I. Arnol'd – författare

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32 produkter

Del 60 - Graduate Texts in Mathematics
Mathematical Methods of Classical Mechanics
AvV.I. Arnol'd
Inbunden, Engelska, 1989
669 kr
Skickas inom 10-15 vardagar
In this text, the author constructs the mathematical apparatus of classical mechanics from the beginning, examining all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the Hamiltonian formalism. This modern approch, based on the theory of the geometry of manifolds, distinguishes iteself from the traditional approach of standard textbooks. Geometrical considerations are emphasized throughout and include phase spaces and flows, vector fields, and Lie groups. The work includes a detailed discussion of qualitative methods of the theory of dynamical systems and of asymptotic methods like perturbation techniques, averaging, and adiabatic invariance.
Ordinary Differential Equations
AvV.I. Arnold
Häftad, Engelska, 1978
936 kr
Skickas inom 5-8 vardagar
Del 250 - Grundlehren der mathematischen Wissenschaften
Geometrical Methods in the Theory of Ordinary Differential Equations
AvV.I. Arnold,Mark Levi
Inbunden, Engelska, 1988
2 182 kr
Skickas inom 10-15 vardagar
Since the first edition of this book, geometrical methods in the theory of ordinary differential equations have become very popular and some progress has been made partly with the help of computers. Much of this progress is represented in this revised, expanded edition, including such topics as the Feigenbaum universality of period doubling, the Zoladec solution, the Iljashenko proof, the Ecalle and Voronin theory, the Varchenko and Hovanski theorems, and the Neistadt theory. In the selection of material for this book, the author explains basic ideas and methods applicable to the study of differential equations. Special efforts were made to keep the basic ideas free from excessive technicalities. Thus the most fundamental questions are considered in great detail, while of the more special and difficult parts of the theory have the character of a survey. Consequently, the reader needs only a general mathematical knowledge to easily follow this text. It is directed to mathematicians, aswell as all users of the theory of differential equations.
Singularities of Differentiable Maps, Volume 1
Classification of Critical Points, Caustics and Wave Fronts
AvV.I. Arnold,S.M. Gusein-Zadem. fl.
Häftad, Engelska, 2012
1 208 kr
Skickas inom 10-15 vardagar
Singularity theory is a far-reaching extension of maxima and minima investigations of differentiable functions, with implications for many different areas of mathematics, engineering (catastrophe theory and the theory of bifurcations), and science. The three parts of this first volume of a two-volume set deal with the stability problem for smooth mappings, critical points of smooth functions, and caustics and wave front singularities. The second volume describes the topological and algebro-geometrical aspects of the theory: monodromy, intersection forms, oscillatory integrals, asymptotics, and mixed Hodge structures of singularities. The first volume has been adapted for the needs of non-mathematicians, presupposing a limited mathematical background and beginning at an elementary level. With this foundation, the book's sophisticated development permits readers to explore more applications than previous books on singularities.
Singularities of Differentiable Maps, Volume 1
Classification of Critical Points, Caustics and Wave Fronts
AvAlexander N. Varchenko,S.M. Gusein-Zadem. fl.
E-bok
PDF, Engelska, 2012
1 570 kr
Läs direkt efter köp
Singularity theory is a far-reaching extension of maxima and minima investigations of differentiable functions, with implications for many different areas of mathematics, engineering (catastrophe theory and the theory of bifurcations), and science. The three parts of this first volume of a two-volume set deal with the stability problem for smooth mappings, critical points of smooth functions, and caustics and wave front singularities. The second volume describes the topological and algebro-geometrical aspects of the theory: monodromy, intersection forms, oscillatory integrals, asymptotics, and mixed Hodge structures of singularities.
The first volume has been adapted for the needs of non-mathematicians, presupposing a limited mathematical background and beginning at an elementary level. With this foundation, the book''s sophisticated development permits readers to explore more applications than previous books on singularities.
Experimental Mathematics
AvV.I. Arnold
Häftad, Engelska, 2015
653 kr
Skickas inom 5-8 vardagar
One of the traditional ways mathematical ideas and even new areas of mathematics are created is from experiments. One of the best-known examples is that of the Fermat hypothesis, which was conjectured by Fermat in his attempts to find integer solutions for the famous Fermat equation. This hypothesis led to the creation of a whole field of knowledge, but it was proved only after several hundred years.This book, based on the author's lectures, presents several new directions of mathematical research. All of these directions are based on numerical experiments conducted by the author, which led to new hypotheses that currently remain open, i.e., are neither proved nor disproved. The hypotheses range from geometry and topology (statistics of plane curves and smooth functions) to combinatorics (combinatorial complexity and random permutations) to algebra and number theory (continuous fractions and Galois groups). For each subject, the author describes the problem and presents numerical results that led him to a particular conjecture. In the majority of cases there is an indication of how the readers can approach the formulated conjectures (at least by conducting more numerical experiments).Written in Arnold's unique style, the book is intended for a wide range of mathematicians, from high school students interested in exploring unusual areas of mathematics on their own, to college and graduate students, to researchers interested in gaining a new, somewhat nontraditional perspective on doing mathematics. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.
Del 60 - Graduate Texts in Mathematics
Mathematical Methods of Classical Mechanics
AvV.I. Arnol'd
Häftad, Engelska, 2010
714 kr
Skickas inom 10-15 vardagar
In this text, the author constructs the mathematical apparatus of classical mechanics from the beginning, examining all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the Hamiltonian formalism. This modern approch, based on the theory of the geometry of manifolds, distinguishes iteself from the traditional approach of standard textbooks. Geometrical considerations are emphasized throughout and include phase spaces and flows, vector fields, and Lie groups. The work includes a detailed discussion of qualitative methods of the theory of dynamical systems and of asymptotic methods like perturbation techniques, averaging, and adiabatic invariance.
Geometrical Methods in the Theory of Ordinary Differential Equations
AvV.I. Arnold,Mark Levi
E-bok
PDF, Engelska, 2012
2 917 kr
Läs direkt efter köp
Since the first edition of this book, geometrical methods in the theory of ordinary differential equations have become very popular and some progress has been made partly with the help of computers. Much of this progress is represented in this revised, expanded edition, including such topics as the Feigenbaum universality of period doubling, the Zoladec solution, the Iljashenko proof, the Ecalle and Voronin theory, the Varchenko and Hovanski theorems, and the Neistadt theory. In the selection of material for this book, the author explains basic ideas and methods applicable to the study of differential equations. Special efforts were made to keep the basic ideas free from excessive technicalities. Thus the most fundamental questions are considered in great detail, while of the more special and difficult parts of the theory have the character of a survey. Consequently, the reader needs only a general mathematical knowledge to easily follow this text. It is directed to mathematicians, aswell as all users of the theory of differential equations.
Singularities of Differentiable Maps
Volume II Monodromy and Asymptotic Integrals
AvS.M. Gusein-Zade,A.N. Varchenkom. fl.
E-bok
PDF, Engelska, 2012
1 728 kr
Läs direkt efter köp
The present. volume is the second volume of the book "Singularities of Differentiable Maps" by V.1. Arnold, A. N. Varchenko and S. M. Gusein-Zade. The first volume, subtitled "Classification of critical points, caustics and wave fronts", was published by Moscow, "Nauka", in 1982. It will be referred to in this text simply as "Volume 1". Whilst the first volume contained the zoology of differentiable maps, that is it was devoted to a description of what, where and how singularities could be encountered, this volume contains the elements of the anatomy and physiology of singularities of differentiable functions. This means that the questions considered in it are about the structure of singularities and how they function. Another distinctive feature of the present volume is that we take a hard look at questions for which it is important to work in the complex domain, where the first volume was devoted to themes for which, on the whole, it was not important which field (real or complex) we were considering. Such topics as, for example, decomposition of singularities, the connection between singularities and Lie algebras and the asymptotic behaviour of different integrals depending on parameters become clearer in the complex domain. The book consists of three parts. In the first part we consider the topological structure of isolated critical points of holomorphic functions. We describe the fundamental topological characteristics of such critical points: vanishing cycles, distinguished bases, intersection matrices, monodromy groups, the variation operator and their interconnections and method of calculation.
Singularities of Differentiable Maps
Volume I: The Classification of Critical Points Caustics and Wave Fronts
AvS.M. Gusein-Zade,A.N. Varchenkom. fl.
E-bok
PDF, Engelska, 2012
710 kr
Läs direkt efter köp
... there is nothing so enthralling, so grandiose, nothing that stuns or captivates the human soul quite so much as a first course in a science. After the first five or six lectures one already holds the brightest hopes, already sees oneself as a seeker after truth. I too have wholeheartedly pursued science passionately, as one would a beloved woman. I was a slave, and sought no other sun in my life. Day and night I crammed myself, bending my back, ruining myself over my books; I wept when I beheld others exploiting science fot personal gain. But I was not long enthralled. The truth is every science has a beginning, but never an end - they go on for ever like periodic fractions. Zoology, for example, has discovered thirty-five thousand forms of life ... A. P. Chekhov. "On the road" In this book a start is made to the "zoology" of the singularities of differentiable maps. This theory is a young branch of analysis which currently occupies a central place in mathematics; it is the crossroads of paths leading from very abstract corners of mathematics (such as algebraic and differential geometry and topology, Lie groups and algebras, complex manifolds, commutative algebra and the like) to the most applied areas (such as differential equations and dynamical systems, optimal control, the theory of bifurcations and catastrophes, short-wave and saddle-point asymptotics and geometrical and wave optics).
Del 250 - Grundlehren der mathematischen Wissenschaften
Geometrical Methods in the Theory of Ordinary Differential Equations
AvV.I. Arnold,Mark Levi
Häftad, Engelska, 2012
2 247 kr
Skickas inom 10-15 vardagar
Since the first edition of this book, geometrical methods in the theory of ordinary differential equations have become very popular and some progress has been made partly with the help of computers. Much of this progress is represented in this revised, expanded edition, including such topics as the Feigenbaum universality of period doubling, the Zoladec solution, the Iljashenko proof, the Ecalle and Voronin theory, the Varchenko and Hovanski theorems, and the Neistadt theory. In the selection of material for this book, the author explains basic ideas and methods applicable to the study of differential equations. Special efforts were made to keep the basic ideas free from excessive technicalities. Thus the most fundamental questions are considered in great detail, while of the more special and difficult parts of the theory have the character of a survey. Consequently, the reader needs only a general mathematical knowledge to easily follow this text. It is directed to mathematicians, aswell as all users of the theory of differential equations.
Del 83 - Monographs in Mathematics
Singularities of Differentiable Maps
Volume II Monodromy and Asymptotic Integrals
AvV.I. Arnold,A.N. Varchenkom. fl.
Häftad, Engelska, 2012
1 420 kr
Skickas inom 10-15 vardagar
The present. volume is the second volume of the book "Singularities of Differentiable Maps" by V.1. Arnold, A. N. Varchenko and S. M. Gusein-Zade. The first volume, subtitled "Classification of critical points, caustics and wave fronts", was published by Moscow, "Nauka", in 1982. It will be referred to in this text simply as "Volume 1". Whilst the first volume contained the zoology of differentiable maps, that is it was devoted to a description of what, where and how singularities could be encountered, this volume contains the elements of the anatomy and physiology of singularities of differentiable functions. This means that the questions considered in it are about the structure of singularities and how they function. Another distinctive feature of the present volume is that we take a hard look at questions for which it is important to work in the complex domain, where the first volume was devoted to themes for which, on the whole, it was not important which field (real or complex) we were considering. Such topics as, for example, decomposition of singularities, the connection between singularities and Lie algebras and the asymptotic behaviour of different integrals depending on parameters become clearer in the complex domain. The book consists of three parts. In the first part we consider the topological structure of isolated critical points of holomorphic functions. We describe the fundamental topological characteristics of such critical points: vanishing cycles, distinguished bases, intersection matrices, monodromy groups, the variation operator and their interconnections and method of calculation.
Del 82 - Monographs in Mathematics
Singularities of Differentiable Maps
Volume I: The Classification of Critical Points Caustics and Wave Fronts
AvV.I. Arnold,A.N. Varchenkom. fl.
Häftad, Engelska, 2011
551 kr
Skickas inom 10-15 vardagar
... there is nothing so enthralling, so grandiose, nothing that stuns or captivates the human soul quite so much as a first course in a science. After the first five or six lectures one already holds the brightest hopes, already sees oneself as a seeker after truth. I too have wholeheartedly pursued science passionately, as one would a beloved woman. I was a slave, and sought no other sun in my life. Day and night I crammed myself, bending my back, ruining myself over my books; I wept when I beheld others exploiting science fot personal gain. But I was not long enthralled. The truth is every science has a beginning, but never an end - they go on for ever like periodic fractions. Zoology, for example, has discovered thirty-five thousand forms of life ... A. P. Chekhov. "On the road" In this book a start is made to the "zoology" of the singularities of differentiable maps. This theory is a young branch of analysis which currently occupies a central place in mathematics; it is the crossroads of paths leading from very abstract corners of mathematics (such as algebraic and differential geometry and topology, Lie groups and algebras, complex manifolds, commutative algebra and the like) to the most applied areas (such as differential equations and dynamical systems, optimal control, the theory of bifurcations and catastrophes, short-wave and saddle-point asymptotics and geometrical and wave optics).
Mathematical Methods of Classical Mechanics
AvV.I. Arnol'd
E-bok
PDF, Engelska, 2013
870 kr
Läs direkt efter köp
In this text, the author constructs the mathematical apparatus of classical mechanics from the beginning, examining all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the Hamiltonian formalism. This modern approch, based on the theory of the geometry of manifolds, distinguishes iteself from the traditional approach of standard textbooks. Geometrical considerations are emphasized throughout and include phase spaces and flows, vector fields, and Lie groups. The work includes a detailed discussion of qualitative methods of the theory of dynamical systems and of asymptotic methods like perturbation techniques, averaging, and adiabatic invariance.
Del 1 - Encyclopaedia of Mathematical Sciences
Dynamical Systems I
Ordinary Differential Equations and Smooth Dynamical Systems
AvD.V. Anosov,S.Kh. Aransonm. fl.
Inbunden, Engelska, 1988
1 092 kr
Skickas inom 10-15 vardagar
From the reviews: "The reading is very easy and pleasant for the non-mathematician, which is really noteworthy. The two chapters enunciate the basic principles of the field, ... indicate connections with other fields of mathematics and sketch the motivation behind the various concepts which are introduced.... What is particularly pleasant is the fact that the authors are quite successful in giving to the reader the feeling behind the demonstrations which are sketched. Another point to notice is the existence of an annotated extended bibliography and a very complete index. This really enhances the value of this book and puts it at the level of a particularly interesting reference tool. I thus strongly recommend to buy this very interesting and stimulating book." Journal de Physique
Del 5 - Encyclopaedia of Mathematical Sciences
Dynamical Systems V
Bifurcation Theory and Catastrophe Theory
AvV.I. Arnold,V.S. Afrajmovichm. fl.
Inbunden, Engelska, 1994
1 092 kr
Skickas inom 10-15 vardagar
Bifurcation theory and catastrophe theory are two well-known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, previously published as Volume 5 of the Encyclopaedia, have given a masterly exposition of these two theories, with penetrating insight.
Del 16 - Encyclopaedia of Mathematical Sciences
Dynamical Systems VII
Integrable Systems Nonholonomic Dynamical Systems
AvV.I. Arnol'd,S.P. Novikov
Inbunden, Engelska, 1993
1 092 kr
Skickas inom 10-15 vardagar
This book is another volume in the successful subseries "Dynamical Systems" of the Encyclopaedia of Mathematical Sciences. It focuses on new developments in the field of integrable systems and it provides a unique and comprehensive survey on new differential geometric and Lie-algebraic methods. Since other literature on these topics is often rather unreadable, this volume will be an indispensable guide to the current research which no mathematician or theoretical physicist who is interested in this field can do without.
Dynamical Systems VIII
Singularity Theory II. Applications
AvV.I. Arnol'd
Inbunden, Engelska, 1993
1 092 kr
Skickas inom 10-15 vardagar
In the first volume of this survey (Arnol'd et al. (1988), hereafter cited as "EMS 6") we acquainted the reader with the basic concepts and methods of the theory of singularities of smooth mappings and functions. This theory has numerous applications in mathematics and physics; here we begin describing these applica tions. Nevertheless the present volume is essentially independent of the first one: all of the concepts of singularity theory that we use are introduced in the course of the presentation, and references to EMS 6 are confined to the citation of technical results. Although our main goal is the presentation of analready formulated theory, the readerwill also come upon some comparatively recent results, apparently unknown even to specialists. We pointout some of these results. 2 3 In the consideration of mappings from C into C in§ 3. 6 of Chapter 1, we define the bifurcation diagram of such a mapping, formulate a K(n, 1)-theorem for the complements to the bifurcation diagrams of simple singularities, give the definition of the Mond invariant N in the spirit of "hunting for invariants", and we draw the reader's attention to a method of constructing the image of a mapping from the corresponding function on a manifold with boundary. In§ 4. 6 of the same chapter we introduce the concept of a versal deformation of a function with a nonisolated singularity in the dass of functions whose critical sets are arbitrary complete intersections of fixed dimension.
Dynamical Systems I
Ordinary Differential Equations and Smooth Dynamical Systems
AvD.V. Anosov,S.Kh. Aransonm. fl.
Häftad, Engelska, 1996
1 092 kr
Skickas inom 10-15 vardagar
From the reviews: "The reading is very easy and pleasant for the non-mathematician, which is really noteworthy. The two chapters enunciate the basic principles of the field, ... indicate connections with other fields of mathematics and sketch the motivation behind the various concepts which are introduced.... What is particularly pleasant is the fact that the authors are quite successful in giving to the reader the feeling behind the demonstrations which are sketched. Another point to notice is the existence of an annotated extended bibliography and a very complete index. This really enhances the value of this book and puts it at the level of a particularly interesting reference tool. I thus strongly recommend to buy this very interesting and stimulating book." Journal de Physique
Del 4 - Encyclopaedia of Mathematical Sciences
Dynamical Systems IV
Symplectic Geometry and its Applications
AvV.I. Arnol'd,S.P. Novikov
Inbunden, Engelska, 2001
1 851 kr
Skickas inom 10-15 vardagar
From the reviews of the first edition:"... In general the articles ... are well written in a style that enables one to grasp the ideas. The actual style is a readable mix of the important results, outlines of proofs and complete proofs when it does not take too long together with readable explanations of what is going on. Also very useful are the large lists of references which are important not only for their mathematical content but also because the references given also contain articles in the Soviet literature which may not be familiar or possibly accessible to readers."New Zealand Math. Soc. Newsletter 1991"... Here ... a wealth of material is displayed for us, too much to even indicate in a review. ... Your reviewer was very impressed by the contents of both volumes (EMS 2 and 4), recommending them without any restriction. As far as he could judge, most presentations seem fairly complete..."Mededelingen van het Wiskundig genootshap 1992
Singularity Theory I
AvV.I. Arnold,V.V. Goryunovm. fl.
Häftad, Engelska, 1998
821 kr
Skickas inom 10-15 vardagar
From the reviews: "... My general impression is of a particularly nice book, with a well-balanced bibliography, recommended!"Mededelingen van Het Wiskundig Genootschap, 1995"... The authors offer here an up to date guide to the topic and its main applications, including a number of new results. It is very convenient for the reader, a carefully prepared and extensive bibliography ... makes it easy to find the necessary details when needed. The books (EMS 6 and EMS 39) describe a lot of interesting topics. ... Both volumes are a very valuable addition to the library of any mathematician or physicist interested in modern mathematical analysis."European Mathematical Society Newsletter, 1994
Dynamical Systems V
Bifurcation Theory and Catastrophe Theory
AvV.I. Arnold,V.S. Afrajmovichm. fl.
Häftad, Engelska, 1999
1 092 kr
Skickas inom 10-15 vardagar
Bifurcation theory and catastrophe theory are two well-known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, previously published as Volume 5 of the Encyclopaedia, have given a masterly exposition of these two theories, with penetrating insight.
Del 16 - Encyclopaedia of Mathematical Sciences
Dynamical Systems VII
Integrable Systems Nonholonomic Dynamical Systems
AvV.I. Arnol'd,S.P. Novikov
Häftad, Engelska, 2010
1 092 kr
Skickas inom 10-15 vardagar
This book is another volume in the successful subseries "Dynamical Systems" of the Encyclopaedia of Mathematical Sciences. It focuses on new developments in the field of integrable systems and it provides a unique and comprehensive survey on new differential geometric and Lie-algebraic methods. Since other literature on these topics is often rather unreadable, this volume will be an indispensable guide to the current research which no mathematician or theoretical physicist who is interested in this field can do without.
Del 39 - Encyclopaedia of Mathematical Sciences
Dynamical Systems VIII
Singularity Theory II. Applications
AvV.I. Arnol'd
Häftad, Engelska, 2010
1 092 kr
Skickas inom 10-15 vardagar
In the first volume of this survey (Arnol'd et al. (1988), hereafter cited as "EMS 6") we acquainted the reader with the basic concepts and methods of the theory of singularities of smooth mappings and functions. This theory has numerous applications in mathematics and physics; here we begin describing these applica tions. Nevertheless the present volume is essentially independent of the first one: all of the concepts of singularity theory that we use are introduced in the course of the presentation, and references to EMS 6 are confined to the citation of technical results. Although our main goal is the presentation of analready formulated theory, the readerwill also come upon some comparatively recent results, apparently unknown even to specialists. We pointout some of these results. 2 3 In the consideration of mappings from C into C in§ 3. 6 of Chapter 1, we define the bifurcation diagram of such a mapping, formulate a K(n, 1)-theorem for the complements to the bifurcation diagrams of simple singularities, give the definition of the Mond invariant N in the spirit of "hunting for invariants", and we draw the reader's attention to a method of constructing the image of a mapping from the corresponding function on a manifold with boundary. In§ 4. 6 of the same chapter we introduce the concept of a versal deformation of a function with a nonisolated singularity in the dass of functions whose critical sets are arbitrary complete intersections of fixed dimension.
Del 4 - Encyclopaedia of Mathematical Sciences
Dynamical Systems IV
Symplectic Geometry and its Applications
AvV.I. Arnol'd,S.P. Novikov
Häftad, Engelska, 2010
1 851 kr
Skickas inom 10-15 vardagar
From the reviews of the first edition:"... In general the articles ... are well written in a style that enables one to grasp the ideas. The actual style is a readable mix of the important results, outlines of proofs and complete proofs when it does not take too long together with readable explanations of what is going on. Also very useful are the large lists of references which are important not only for their mathematical content but also because the references given also contain articles in the Soviet literature which may not be familiar or possibly accessible to readers."New Zealand Math. Soc. Newsletter 1991"... Here ... a wealth of material is displayed for us, too much to even indicate in a review. ... Your reviewer was very impressed by the contents of both volumes (EMS 2 and 4), recommending them without any restriction. As far as he could judge, most presentations seem fairly complete..."Mededelingen van het Wiskundig genootshap 1992
Dynamical Systems V
Bifurcation Theory and Catastrophe Theory
AvL.P. Shil'nikov,Yu.S. Il'yashenkom. fl.
E-bok
PDF, Engelska, 2013
1 427 kr
Läs direkt efter köp
Bifurcation theory and catastrophe theory are two well-known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970''s, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, previously published as Volume 5 of the Encyclopaedia, have given a masterly exposition of these two theories, with penetrating insight.
Singularity Theory I
AvV.A. Vasil'ev,O.V. Lyashkom. fl.
E-bok
PDF, Engelska, 2012
1 026 kr
Läs direkt efter köp
From the reviews: "... My general impression is of a particularly nice book, with a well-balanced bibliography, recommended!"Mededelingen van Het Wiskundig Genootschap, 1995"... The authors offer here an up to date guide to the topic and its main applications, including a number of new results. It is very convenient for the reader, a carefully prepared and extensive bibliography ... makes it easy to find the necessary details when needed. The books (EMS 6 and EMS 39) describe a lot of interesting topics. ... Both volumes are a very valuable addition to the library of any mathematician or physicist interested in modern mathematical analysis."European Mathematical Society Newsletter, 1994
Mathematical Aspects of Classical and Celestial Mechanics
AvA.I. Neishtadt,Victor V. Kozlovm. fl.
E-bok
PDF, Engelska, 2013
1 136 kr
Läs direkt efter köp
From the reviews: "... As an encyclopaedia article, this book does not seek to serve as a textbook, nor to replace the original articles whose results it describes. The book''s goal is to provide an overview, pointing out highlights and unsolved problems, and putting individual results into a coherent context. It is full of historical nuggets, many of them surprising. ... The examples are especially helpful; if a particular topic seems difficult, a later example frequently tames it. The writing is refreshingly direct, never degenerating into a vocabulary lesson for its own sake. The book accomplishes the goals it has set for itself. While it is not an introduction to the field, it is an excellent overview. ..." American Mathematical Monthly, Nov. 1989"This is a book to curl up with in front of a fire on a cold winter''s evening. ..." SIAM Reviews, Sept. 1989
Dynamical Systems IV
Symplectic Geometry and its Applications
AvS.P. Novikov,V.I. Arnol'd
E-bok
PDF, Engelska, 2013
2 384 kr
Läs direkt efter köp
From the reviews of the first edition:"... In general the articles ... are well written in a style that enables one to grasp the ideas. The actual style is a readable mix of the important results, outlines of proofs and complete proofs when it does not take too long together with readable explanations of what is going on. Also very useful are the large lists of references which are important not only for their mathematical content but also because the references given also contain articles in the Soviet literature which may not be familiar or possibly accessible to readers."New Zealand Math. Soc. Newsletter 1991"... Here ... a wealth of material is displayed for us, too much to even indicate in a review. ... Your reviewer was very impressed by the contents of both volumes (EMS 2 and 4), recommending them without any restriction. As far as he could judge, most presentations seem fairly complete..."Mededelingen van het Wiskundig genootshap 1992
Dynamical Systems IV
Symplectic Geometry and its Applications
AvS.P. Novikov,V.I. Arnol'd
E-bok
PDF, Engelska, 2013
1 136 kr
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This book takes a snapshot of the mathematical foundations of classical and quantum mechanics from a contemporary mathematical viewpoint. It covers a number of important recent developments in dynamical systems and mathematical physics and places them in the framework of the more classical approaches; the presentation is enhanced by many illustrative examples concerning topics which have been of especial interest to workers in the field, and by sketches of the proofs of the major results. The comprehensive bibliographies are designed to permit the interested reader to retrace the major stages in the development of the field if he wishes. Not so much a detailed textbook for plodding students, this volume, like the others in the series, is intended to lead researchers in other fields and advanced students quickly to an understanding of the ''state of the art'' in this area of mathematics. As such it will serve both as a basic reference work on important areas of mathematical physics as they stand today, and as a good starting point for further, more detailed study for people new to this field.

V.I. Arnol'd – författare

Mathematical Methods of Classical Mechanics

Ordinary Differential Equations

Geometrical Methods in the Theory of Ordinary Differential Equations

Singularities of Differentiable Maps, Volume 1

Singularities of Differentiable Maps, Volume 1

Experimental Mathematics

Mathematical Methods of Classical Mechanics

Geometrical Methods in the Theory of Ordinary Differential Equations

Singularities of Differentiable Maps

Singularities of Differentiable Maps

Geometrical Methods in the Theory of Ordinary Differential Equations

Singularities of Differentiable Maps

Singularities of Differentiable Maps

Mathematical Methods of Classical Mechanics

Dynamical Systems I

Dynamical Systems V

Dynamical Systems VII

Dynamical Systems VIII

Dynamical Systems I

Dynamical Systems IV

Singularity Theory I

Dynamical Systems V

Dynamical Systems VII

Dynamical Systems VIII

Dynamical Systems IV

Dynamical Systems V

Singularity Theory I

Mathematical Aspects of Classical and Celestial Mechanics

Dynamical Systems IV

Dynamical Systems IV