## Givental, Alexander B.

# Vladimir I. Arnold - Collected Works

**Table of contents**

1. A Variational principle for three-dimensional steady flows of an ideal fluid*Vladimir I. Arnold*

2. On the Riemann curvature of diffeomorphism groups*Vladimir I. Arnold*

3. Sur la topologie des écoulements stationnaires des fluides parfaits*Vladimir I. Arnold*

4. Conditions for non-linear stability of stationary plane curvilinear flows of an ideal fluid*Vladimir I. Arnold*

5. On the topology of three-dimensional steady flows of an ideal fluid*Vladimir I. Arnold*

6. On an a priori estimate in the theory of hydrodynamical stability*Vladimir I. Arnold*

7. On the differential geometry of infinite-dimensional Lie groups and its application to the hydrodynamics of perfect fluids*Vladimir I. Arnold*

8. On a variational principle for the steady flows of perfect fluids and its application to problems of non-linear stability*Vladimir I. Arnold*

9. On a characteristic class arising in quantization conditions*Vladimir I. Arnold*

10. A note on the Weierstrass preparation theorem*Vladimir I. Arnold*

11. The stability problem and ergodic properties for classical dynamical systems*Vladimir I. Arnold*

12. A remark on the ramification of hyperelliptic integrals as functions of parameters*Vladimir I. Arnold*

13. Singularities of smooth mappings*Vladimir I. Arnold*

14. Remarks on singularities of finite codimension in complex dynamical systems*Vladimir I. Arnold*

15. Braids of algebraic functions and the cohomology of swallowtails*Vladimir I. Arnold*

16. Hamiltonian nature of the Euler equations in the dynamics of a rigid body and of an ideal fluid*Vladimir I. Arnold*

17. On one-dimensional cohomology of the Lie algebra of divergence-free vector fields and on rotation numbers of dynamic systems*Vladimir I. Arnold*

18. The cohomology ring of the colored braid group*Vladimir I. Arnold*

19. On cohomology classes of algebraic functions invariant under Tschirnhausen transformations*Vladimir I. Arnold*

20. Trivial problems*Vladimir I. Arnold*

21. Local problems of analysis*Vladimir I. Arnold*

22. Algebraic unsolvability of the problem of stability and the problem of the topological classification of the singular points of analytic systems of differential equations*Vladimir I. Arnold*

23. On some topological invariants of algebraic functions*Vladimir I. Arnold*

24. Topological invariants of algebraic functions II*Vladimir I. Arnold*

25. Algebraic unsolvability of the problem of Lyapunov stability and the problem of topological classification of singular points of an analytic system of differential equations*Vladimir I. Arnold*

26. On the arrangement of ovals of real plane algebraic curves, involutions of four-dimensional smooth manifolds, and the arithmetic of integral quadratic forms*Vladimir I. Arnold*

27. The topology of real algebraic curves*Vladimir I. Arnold*

28. On matrices depending on parameters*Vladimir I. Arnold*

29. Lectures on bifurcations in versal families*Vladimir I. Arnold*

30. Versal families and bifurcations of differential equations*Vladimir I. Arnold*

31. Remarks on the behaviour of flow of a three-dimensional perfect fluid in the presence of a small perturbation of the initial velocity field*Vladimir I. Arnold*

32. The asymptotic Hopf invariant and its applications*Vladimir I. Arnold*

33. A magnetic field in a moving conducting fluid*Vladimir I. Arnold*

34. A magnetic field in a stationary flow with stretching in a Riemannian manifold fluid*Vladimir I. Arnold*

35. Stationary magnetic field in a periodic flow fluid*Vladimir I. Arnold*

36. Some remarks on the antidynamo theorem*Vladimir I. Arnold*

37. Evolution of a magnetic field under the action of transfer and diffusion*Vladimir I. Arnold*

38. The growth of a magnetic field in a three-dimensional steady incompressible flow*Vladimir I. Arnold*

39. Evolution of a magnetic field under the action of drift and diffusion*Vladimir I. Arnold*

40. Exponential scattering of trajectories and its hydrodynamical applications*Vladimir I. Arnold*

41. Kolmogorov’s hydrodynamic attractors*Vladimir I. Arnold*

42. Topological methods in hydrodynamics*Vladimir I. Arnold*

43. Translator’s Preface to J. Milnor’s book ″Morse Theory″*Vladimir I. Arnold*

44. Henri Poincaré: Selected Works in Three Volumes. Vol. I New Methods of Celestial Mechanics - Preface. From the editorial board. Comments*Vladimir I. Arnold*

45. Comments on the paper “On a geometric theorem” by Henri Poincaré*Vladimir I. Arnold*

**Keywords:** Mathematics, Mathematical Applications in the Physical Sciences, Algebraic Geometry, Mathematical Methods in Physics

- Author(s)
- Givental, Alexander B.
- Khesin, Boris A.
- Varchenko, Alexander N.
- Vassiliev, Victor A.
- Viro, Oleg Ya.
- Arnold, Vladimir I.
- Publisher
- Springer
- Publication year
- 2014
- Language
- en
- Edition
- 2014
- Series
- Vladimir I. Arnold - Collected Works
- Category
- Natural Sciences
- Format
- Ebook
- eISBN (PDF)
- 9783642310317