Vladimir I. Arnold - Collected Works

Table of Contents

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   Book Overview
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   Chapter 1 A Variational principle for three-dimensional steady flows of an ideal fluid
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   Chapter 2 On the Riemann curvature of diffeomorphism groups
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   Chapter 3 Sur la topologie des écoulements stationnaires des fluides parfaits
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   Chapter 4 Conditions for non-linear stability of stationary plane curvilinear flows of an ideal fluid
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   Chapter 5 On the topology of three-dimensional steady flows of an ideal fluid
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   Chapter 6 On an a priori estimate in the theory of hydrodynamical stability
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   Chapter 7 On the differential geometry of infinite-dimensional Lie groups and its application to the hydrodynamics of perfect fluids
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   Chapter 8 On a variational principle for the steady flows of perfect fluids and its application to problems of non-linear stability
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    Chapter 9 On a characteristic class arising in quantization conditions
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    Chapter 10 A note on the Weierstrass preparation theorem
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    Chapter 11 The stability problem and ergodic properties for classical dynamical systems
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    Chapter 12 A remark on the ramification of hyperelliptic integrals as functions of parameters
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    Chapter 13 Singularities of smooth mappings
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    Chapter 14 Remarks on singularities of finite codimension in complex dynamical systems
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    Chapter 15 Braids of algebraic functions and the cohomology of swallowtails
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    Chapter 16 Hamiltonian nature of the Euler equations in the dynamics of a rigid body and of an ideal fluid
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    Chapter 17 On one-dimensional cohomology of the Lie algebra of divergence-free vector fields and on rotation numbers of dynamic systems
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    Chapter 18 The cohomology ring of the colored braid group
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    Chapter 19 On cohomology classes of algebraic functions invariant under Tschirnhausen transformations
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    Chapter 20 Trivial problems
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    Chapter 21 Local problems of analysis
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    Chapter 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
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    Chapter 23 On some topological invariants of algebraic functions
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    Chapter 24 Topological invariants of algebraic functions II
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    Chapter 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
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    Chapter 26 On the arrangement of ovals of real plane algebraic curves, involutions of four-dimensional smooth manifolds, and the arithmetic of integral quadratic forms
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    Chapter 27 The topology of real algebraic curves
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    Chapter 28 On matrices depending on parameters
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    Chapter 29 Lectures on bifurcations in versal families
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    Chapter 30 Versal families and bifurcations of differential equations
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    Chapter 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
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    Chapter 32 The asymptotic Hopf invariant and its applications
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    Chapter 33 A magnetic field in a moving conducting fluid
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    Chapter 34 A magnetic field in a stationary flow with stretching in a Riemannian manifold fluid
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    Chapter 35 Stationary magnetic field in a periodic flow fluid
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    Chapter 36 Some remarks on the antidynamo theorem
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    Chapter 37 Evolution of a magnetic field under the action of transfer and diffusion
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    Chapter 38 The growth of a magnetic field in a three-dimensional steady incompressible flow
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    Chapter 39 Evolution of a magnetic field under the action of drift and diffusion
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    Chapter 40 Exponential scattering of trajectories and its hydrodynamical applications
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    Chapter 41 Kolmogorov’s hydrodynamic attractors
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    Chapter 42 Topological methods in hydrodynamics
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    Chapter 43 Translator’s Preface to J. Milnor’s book ″Morse Theory″
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    Chapter 44 Henri Poincaré: Selected Works in Three Volumes. Vol. I New Methods of Celestial Mechanics - Preface. From the editorial board. Comments
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    Chapter 45 Comments on the paper “On a geometric theorem” by Henri Poincaré