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7 produkter
7 produkter
1 381 kr
Skickas inom 10-15 vardagar
This book offers the first systematic account of canard cycles, an intriguing phenomenon in the study of ordinary differential equations. The canard cycles are treated in the general context of slow-fast families of two-dimensional vector fields. The central question of controlling the limit cycles is addressed in detail and strong results are presented with complete proofs.In particular, the book provides a detailed study of the structure of the transitions near the critical set of non-isolated singularities. This leads to precise results on the limit cycles and their bifurcations, including the so-called canard phenomenon and canard explosion. The book also provides a solid basis for the use of asymptotic techniques. It gives a clear understanding of notions like inner and outer solutions, describing their relation and precise structure.The first part of the book provides a thorough introduction to slow-fast systems, suitable for graduate students. The second and third parts will be of interest to both pure mathematicians working on theoretical questions such as Hilbert's 16th problem, as well as to a wide range of applied mathematicians looking for a detailed understanding of two-scale models found in electrical circuits, population dynamics, ecological models, cellular (FitzHugh–Nagumo) models, epidemiological models, chemical reactions, mechanical oscillators with friction, climate models, and many other models with tipping points.
1 136 kr
Skickas inom 5-8 vardagar
This book offers the first systematic account of canard cycles, an intriguing phenomenon in the study of ordinary differential equations. The canard cycles are treated in the general context of slow-fast families of two-dimensional vector fields. The central question of controlling the limit cycles is addressed in detail and strong results are presented with complete proofs.In particular, the book provides a detailed study of the structure of the transitions near the critical set of non-isolated singularities. This leads to precise results on the limit cycles and their bifurcations, including the so-called canard phenomenon and canard explosion. The book also provides a solid basis for the use of asymptotic techniques. It gives a clear understanding of notions like inner and outer solutions, describing their relation and precise structure.The first part of the book provides a thorough introduction to slow-fast systems, suitable for graduate students. The second and third parts will be of interest to both pure mathematicians working on theoretical questions such as Hilbert's 16th problem, as well as to a wide range of applied mathematicians looking for a detailed understanding of two-scale models found in electrical circuits, population dynamics, ecological models, cellular (FitzHugh–Nagumo) models, epidemiological models, chemical reactions, mechanical oscillators with friction, climate models, and many other models with tipping points.
536 kr
Skickas inom 10-15 vardagar
In a coherent, exhaustive and progressive way, this book presents the tools for studying local bifurcations of limit cycles in families of planar vector fields. A systematic introduction is given to such methods as division of an analytic family of functions in its ideal of coefficients, and asymptotic expansion of non-differentiable return maps and desingularisation. The exposition moves from classical analytic geometric methods applied to regular limit periodic sets to more recent tools for singular limit sets.The methods can be applied to theoretical problems such as Hilbert's 16th problem, but also for the purpose of establishing bifurcation diagrams of specific families as well as explicit computations.- - -The book as a whole is a well-balanced exposition that can be recommended to all those who want to gain a thorough understanding and proficiency in the recently developed methods. The book, reflecting the current state of the art, can also be used for teaching special courses. (Mathematical Reviews)
Del 164 - Modern Birkhäuser Classics
Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem
Häftad, Engelska, 2012
536 kr
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In a coherent, exhaustive and progressive way, this book presents the tools for studying local bifurcations of limit cycles in families of planar vector fields. A systematic introduction is given to such methods as division of an analytic family of functions in its ideal of coefficients, and asymptotic expansion of non-differentiable return maps and desingularisation. The exposition moves from classical analytic geometric methods applied to regular limit periodic sets to more recent tools for singular limit sets.The methods can be applied to theoretical problems such as Hilbert's 16th problem, but also for the purpose of establishing bifurcation diagrams of specific families as well as explicit computations.- - -The book as a whole is a well-balanced exposition that can be recommended to all those who want to gain a thorough understanding and proficiency in the recently developed methods. The book, reflecting the current state of the art, can also be used for teaching special courses. (Mathematical Reviews)
Del 1455 - Lecture Notes in Mathematics
Bifurcations of Planar Vector Fields
Proceedings of a Meeting held in Luminy, France, Sept. 18-22, 1989
Häftad, Engelska, 1990
377 kr
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A collection of papers on differential equations and dynamical systems which stresses topics relating to Hilbert's 16th problem. Among these are a solution to Dulac's problem, results on the multiplicity of singular cycles and results on the zeroes of abelian integrals.
Del 1480 - Lecture Notes in Mathematics
Bifurcations of Planar Vector Fields
Nilpotent Singularities and Abelian Integrals
Häftad, Engelska, 1991
483 kr
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This monograph reports on recent work by the authors on the bifurcation structure of singular points of planar vector fields whose linear parts are nilpotent. The bifurcation diagrams of the most important codimension cases are studied in detail. The results presented intend to reach the limits of what is currently known on the bifurcation theory of planar vector fields. While the treatment is geometric, special analytical tools using abelian integrals are needed, and are explicitly developed. The reader is assumed to be familiar with the elements of bifurcation and dynamical systems theory. The book is addressed to researchers and graduate students working in ordinary differential equations and dynamical systems, as well as anyone modelling complex multiparametric phenomena.
Del 164 - Modern Birkhäuser Classics
Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem
Inbunden, Engelska, 1998
536 kr
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r Presents the tools for studying local bifurcations of limit cycles in families of planar vector fields. The text provides a systematic introduction to such methods as division of an analytic family of functions in its ideal of coefficients and asymptotic expansion of non-differentiable return maps and desingularisation. The exposision moves from classical analytic geometric methods to regular limit periodic sets to more recent tools for singular limit sets.