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Vladimir I. Arnold - Collected Works

Hydrodynamics, Bifurcation Theory, and Algebraic Geometry 1965-1972

  • Book
  • © 2014

Overview

Authors:
  1. Vladimir I. Arnold

    1. Russian Academy of Sciences Steklov Mathematical Institute, Moscow, Russia

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Editors:
  1. Alexander B. Givental

    1. Department of Mathematics, University of California, Berkeley, USA

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  2. Boris A. Khesin

    1. Department of Mathematics, University of Toronto, Toronto, Canada

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  3. Alexander N. Varchenko

    1. Department of Mathematics, University of North Carolina, Chapel Hill, USA

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  4. Victor A. Vassiliev

    1. Dept. Probability Theory & Mathematical Statistics, Russian Academy of Sciences Steklov Mathematical Institute, Moscow, Russia

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  5. Oleg Ya. Viro

    1. Institute for Mathematical Sciences, Stony Brook University, Stony Brook, USA

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  • Collected Works of one of the most outstanding mathematicians of all times
  • Arnold was recipient of many awards
  • Wrote more than 700 papers and many books
  • 19 notions named after Arnold
  • Second volume of an ongoing project of putting together Arnold's work

Part of the book series: Vladimir I. Arnold - Collected Works (ARNOLD)

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Table of contents (45 chapters)

  1. Front Matter

    Pages I-XIII
    Download chapter PDF

  2. A Variational principle for three-dimensional steady flows of an ideal fluid

    • Vladimir I. Arnold
    Pages 1-7

  3. On the Riemann curvature of diffeomorphism groups

    • Vladimir I. Arnold
    Pages 9-13

  4. Sur la topologie des écoulements stationnaires des fluides parfaits

    • Vladimir I. Arnold
    Pages 15-18

  5. Conditions for non-linear stability of stationary plane curvilinear flows of an ideal fluid

    • Vladimir I. Arnold
    Pages 19-23

  6. On the topology of three-dimensional steady flows of an ideal fluid

    • Vladimir I. Arnold
    Pages 25-28

  7. On an a priori estimate in the theory of hydrodynamical stability

    • Vladimir I. Arnold
    Pages 29-31

  8. On the differential geometry of infinite-dimensional Lie groups and its application to the hydrodynamics of perfect fluids

    • Vladimir I. Arnold
    Pages 33-69

  9. On a variational principle for the steady flows of perfect fluids and its application to problems of non-linear stability

    • Vladimir I. Arnold
    Pages 71-84

  10. On a characteristic class arising in quantization conditions

    • Vladimir I. Arnold
    Pages 85-97

  11. A note on the Weierstrass preparation theorem

    • Vladimir I. Arnold
    Pages 99-105

  12. The stability problem and ergodic properties for classical dynamical systems

    • Vladimir I. Arnold
    Pages 107-113

  13. A remark on the ramification of hyperelliptic integrals as functions of parameters

    • Vladimir I. Arnold
    Pages 115-118

  14. Singularities of smooth mappings

    • Vladimir I. Arnold
    Pages 119-161

  15. Remarks on singularities of finite codimension in complex dynamical systems

    • Vladimir I. Arnold
    Pages 163-170

  16. Braids of algebraic functions and the cohomology of swallowtails

    • Vladimir I. Arnold
    Pages 171-173

  17. Hamiltonian nature of the Euler equations in the dynamics of a rigid body and of an ideal fluid

    • Vladimir I. Arnold
    Pages 175-178

  18. On one-dimensional cohomology of the Lie algebra of divergence-free vector fields and on rotation numbers of dynamic systems

    • Vladimir I. Arnold
    Pages 179-182

  19. The cohomology ring of the colored braid group

    • Vladimir I. Arnold
    Pages 183-186

  20. On cohomology classes of algebraic functions invariant under Tschirnhausen transformations

    • Vladimir I. Arnold
    Pages 187-190
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Keywords

About this book

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.

Reviews

“Volume II focuses on hydrodynamics, bifurcation theory and algebraic geometry. … Arnold was a very prolific writer. The publication of his collected works is a huge task and a great service to the mathematical community particularly since his papers appeared in various journals some of which are not easily accessible. … I have no doubt that these volumes will be of great benefit to the current and future generations of researchers and graduate students.” (Gerard Misiołek, zbMATH 1354.01038, 2017)

Authors, Editors and Affiliations

  • Department of Mathematics, University of California, Berkeley, USA

    Alexander B. Givental

  • Department of Mathematics, University of Toronto, Toronto, Canada

    Boris A. Khesin

  • Department of Mathematics, University of North Carolina, Chapel Hill, USA

    Alexander N. Varchenko

  • Dept. Probability Theory & Mathematical Statistics, Russian Academy of Sciences Steklov Mathematical Institute, Moscow, Russia

    Victor A. Vassiliev

  • Institute for Mathematical Sciences, Stony Brook University, Stony Brook, USA

    Oleg Ya. Viro

  • Russian Academy of Sciences Steklov Mathematical Institute, Moscow, Russia

    Vladimir I. Arnold

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