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Collected Works, Volume II: Hydrodynamics, Bifurcation Theory, and Algebraic Geometry 1965-1972

Vladimir I. Arnold
Publication Date: 
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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.