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Givental, Alexander B.

Vladimir I. Arnold - Collected Works

Givental, Alexander B. - Vladimir I. Arnold - Collected Works, ebook

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ISBN: 9783642310317
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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)
 
 
 
 
 
Publisher
Springer
Publication year
2014
Language
en
Edition
2014
Series
Vladimir I. Arnold - Collected Works
Category
Natural Sciences
Format
Ebook
eISBN (PDF)
9783642310317

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