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# Vladimir I. Arnold - Collected Works , Vol. II

We do not plan to review this book.

1 Variational principle for three-dimensional steady-state flows of an ideal fluid

2 On the Riemann curvature of diffeomorphism groups

3 Sur la topologie des écoulements stationnaires des fluides parfaits (in French)

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

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

6 On an a priori estimate in the theory of hydrodynamical stability

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

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

9 Characteristic class entering in quantization conditions

10 A note on Weierstrass auxiliary theorem

11 A letter to the editors (in Russian)

12 The stability problem and ergodic properties for classical dynamical systems

13 Remark on the branching of hyperelliptic integrals as functions of the parameters

14 Singularities of smooth mappings

15 Braids of algebraic functions and the cohomology of swallowtails

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

17 Remarks on singularities of finite codimension in complex dynamical systems

18 One-dimensional cohomologies of the Lie algebras of non-divergence vector fields, and rotation numbers of dynamic systems

19 The cohomology ring of the colored braid group

20 Trivial problems

21 Cohomology classes of algebraic functions invariant under Tschirnhausen transformations

22 Local Problems of Analysis

23 Algebraic unsolvability of the problem of stability and the problem of the topological classification of the singular points of analytic systems of differential equations (in Russian)

24 On some topological invariants of algebraic functions

25 Topological invariants of algebraic functions II

26 Algebraic unsolvability of the problem of Ljapunov stability and the problem of the topological classification of singular points of an analytic system of differential equations

27 On matrices depending on parameters

28 Distribution of ovals of the real plane of algebraic curves of involutions of four-dimensional smooth manifolds and the arithmetic of integer valued quadratic forms

29 Versal families and bifurcations of differential equations (in Russian)

30 Notes on the three-dimensional flow pattern of a perfect fluid in the presence of a small perturbation of the initial velocity field

31 Lectures on bifurcations in versal families

32 The topology of real algebraic curves (in Russian)

33 The asymptotic Hopf invariant and its applications

34 Magnetic field in a moving conducting fluid

35 A magnetic field in a stationary flow with stretching in a Riemannian space

36 The large-scale structure of the universe I. General properties. One- and two-dimensional models

37 Elements of the large-scale structure of the universe

38 Some remarks on the antidynamo theorem

39 Steady-state magnetic field in a periodic flow

40 Evolution of a magnetic field under the action of transfer and diffusion

41 The growth of a magnetic field in a three-dimensional steady incompressible fluid

42 Evolution of a magnetic field under the action of drift and diffusion (in Russian)

43 Exponential scattering of trajectories and its hydrodynamical applications

44 Kolmogorov's hydrodynamic attractors

45 Topological methods in hydrodynamics

46 Problemes mathématiques de l'hydrodynamique et de la magnétohydrodynamique (in English)

47 Translator's Preface to J. Milnor's book "Morse Theory"

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

49 Comments on the paper "On a geometric theorem" by Henri Poincaré.

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