Vladimir I. Arnold - Collected Works

1. Front Matter

   Pages I-XIII

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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

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.

• Algebraic Geometry
• Bifurcation Theory
• Hydrodynamics

“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)

• 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

Policies and ethics