Boris A. Khesin - Böcker

The first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. The book is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry.

First published in 1998 this unique monograph treats topological, group-theoretic, and geometric problems of ideal hydrodynamics and magneto-hydrodynamics from a unified point of view. It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures.

First published in 1998 this unique monograph treats topological, group-theoretic, and geometric problems of ideal hydrodynamics and magneto-hydrodynamics from a unified point of view. It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures.

This volume 6 of the Collected Works comprises 27 papers by V.I.Arnold, one of the most outstanding mathematicians of all times, written in 1991 to 1995. During this period Arnold's interests covered Vassiliev’s theory of invariants and knots, invariants and bifurcations of plane curves,   combinatorics of Bernoulli, Euler and Springer numbers,   geometry of wave fronts, the Berry phase and quantum Hall effect.The articles include a list of problems in dynamical systems, a discussion of the problem of (in)solvability of equations, papers on symplectic geometry of caustics and contact  geometry of wave fronts, comments on problems of A.D.Sakharov, as well as a rather unusual paper on projective topology. The interested reader will certainly enjoy Arnold’s 1994 paper on mathematical problems in physics with the opening by-now famous phrase “Mathematics is the name for those domains of theoretical physics that are temporarily unfashionable.”The book will be of interest to the wide audience  from college students to professionals in mathematics or physics and in the history of science. The volume also includes translations of two interviews given by Arnold to the French and Spanish media. One can see how worried he was about the fate of Russian and world mathematics and science in general.

This volume 6 of the Collected Works comprises 27 papers by V.I.Arnold, one of the most outstanding mathematicians of all times, written in 1991 to 1995. During this period Arnold's interests covered Vassiliev’s theory of invariants and knots, invariants and bifurcations of plane curves,   combinatorics of Bernoulli, Euler and Springer numbers,   geometry of wave fronts, the Berry phase and quantum Hall effect.The articles include a list of problems in dynamical systems, a discussion of the problem of (in)solvability of equations, papers on symplectic geometry of caustics and contact  geometry of wave fronts, comments on problems of A.D.Sakharov, as well as a rather unusual paper on projective topology. The interested reader will certainly enjoy Arnold’s 1994 paper on mathematical problems in physics with the opening by-now famous phrase “Mathematics is the name for those domains of theoretical physics that are temporarily unfashionable.”The book will be of interest to the wide audience  from college students to professionals in mathematics or physics and in the history of science. The volume also includes translations of two interviews given by Arnold to the French and Spanish media. One can see how worried he was about the fate of Russian and world mathematics and science in general.

Arnold’s work during this period covers symplectic topology, contact geometry and wave propagation, quasicrystals, dynamics of intersections, bifurcations, and catastrophe theory. He was seriously concerned with decaying mathematical education in Russia and worldwide — one can see this in several articles translated for this volume.

This volume 5 of the Collected Works includes papers written by V.I. Arnold, one of the most outstanding mathematicians of all times, during the period from 1986 to 1991. Arnold’s work during this period covers symplectic topology, contact geometry and wave propagation, quasicrystals, dynamics of intersections, bifurcations, and catastrophe theory.He was seriously concerned with decaying mathematical education in Russia and worldwide — one can see this in several articles translated for this volume. Of particular interest are the sets of problems which Arnold collected under the name “Mathematical Trivium” — in his opinion, any math or physics university graduate should be able to solve any problem from that list. The reader will also enjoy perusing several interviews with Arnold, as well as his remarkable warm memories about Ya.B. Zeldovich and his teacher A.N. Kolmogorov. One of Arnold’s papers on catastrophe theory translated for this volume also contains a beautiful translation of E.A. Baratynsky’s poem made by A.B. Givental.The book will be of interest to the wide audience from college students to professionals in mathematics or physics and in the history of science.

This volume completes the seven-volume project of “Collected Works of Vladimir Arnold", the first volume of which was published in 2009.

This volume 7 of the “Collected Works" includes papers written by V.I. Arnold, one of the most outstanding mathematicians of all times,  during the period from 1996 to 1999. At that time Arnold was focusing on the description of various spaces of curves, higher-dimensional continued fractions, pseudoperiodic topology, and unifying ideas related to symplectization, complexification and mathematical trinities in topology and mathematics in general. The “Arnoldfest" conference celebrating 60th anniversary of V.Arnold took place at the Fields Institute and University of Toronto, Canada, in 1997,  and Arnold's lectures at that conference are included in this volume. In the 1990s Arnold got increasingly concerned with the decay of science and math education in many Western countries, and his publications fighting “the victorious march of the antiscientific revolution" (as he phrased it in one of his papers) are collected in this volume as well. Some of Arnold's writings stimulated others to write supplements with more detail, and the volume also includes the notes of A.M.Vershik, J.K.Moser, and B.A.Khesin. Finally, a glimpse of Arnold's personality can also be appreciated in a little gem, his short article devoted to resolving the mystery of the origin of the epigraph to “Eugene Onegin" by A.S. Pushkin, a famous XIXth century Russian poet.  The book will be of interest to the wide audience  from college students to professionals in mathematics or physics and in the history of science. This volume completes the seven-volume project of “Collected Works of Vladimir Arnold", the first volume of which was published in 2009. Arnold's publications in the 2000s were also abundant, he turned to new topics, wrote several books, he gave numerous lectures, both research and educational. But what has already been published in these seven volumes is a treasure trove, an ocean of ideas, methods, and results, and this is now before the reader to explore. Happy voyage!

Vladimir Arnold was one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. At the same time he is one of the most prolific and outstanding mathematical authors. This second volume of his Collected Works focuses on hydrodynamics, bifurcation theory, and algebraic geometry.