Vladimir I. Arnold - Collected Works: Hydrodynamics, Bifurcation Theory, and Algebraic Geometry 1965-1972

Front Matter....Pages I-XIII
A Variational principle for three-dimensional steady flows of an ideal fluid....Pages 1-7
On the Riemann curvature of diffeomorphism groups....Pages 9-13
Sur la topologie des écoulements stationnaires des fluides parfaits....Pages 15-18
Conditions for non-linear stability of stationary plane curvilinear flows of an ideal fluid....Pages 19-23
On the topology of three-dimensional steady flows of an ideal fluid....Pages 25-28
On an a priori estimate in the theory of hydrodynamical stability....Pages 29-31
On the differential geometry of infinite-dimensional Lie groups and its application to the hydrodynamics of perfect fluids....Pages 33-69
On a variational principle for the steady flows of perfect fluids and its application to problems of non-linear stability....Pages 71-84
On a characteristic class arising in quantization conditions....Pages 85-97
A note on the Weierstrass preparation theorem....Pages 99-105
The stability problem and ergodic properties for classical dynamical systems....Pages 107-113
A remark on the ramification of hyperelliptic integrals as functions of parameters....Pages 115-118
Singularities of smooth mappings....Pages 119-161
Remarks on singularities of finite codimension in complex dynamical systems....Pages 163-170
Braids of algebraic functions and the cohomology of swallowtails....Pages 171-173
Hamiltonian nature of the Euler equations in the dynamics of a rigid body and of an ideal fluid....Pages 175-178
On one-dimensional cohomology of the Lie algebra of divergence-free vector fields and on rotation numbers of dynamic systems....Pages 179-182
The cohomology ring of the colored braid group....Pages 183-186
On cohomology classes of algebraic functions invariant under Tschirnhausen transformations....Pages 187-190
Trivial problems....Pages 191-191
Local problems of analysis....Pages 193-196
Algebraic unsolvability of the problem of stability and the problem of the topological classification of the singular points of analytic systems of differential equations....Pages 197-198
On some topological invariants of algebraic functions....Pages 199-221
Topological invariants of algebraic functions II....Pages 223-230
Algebraic unsolvability of the problem of Lyapunov stability and the problem of topological classification of singular points of an analytic system of differential equations....Pages 231-238
On the arrangement of ovals of real plane algebraic curves, involutions of four-dimensional smooth manifolds, and the arithmetic of integral quadratic forms....Pages 239-249
The topology of real algebraic curves....Pages 251-253
On matrices depending on parameters....Pages 255-269
Lectures on bifurcations in versal families....Pages 271-340
Versal families and bifurcations of differential equations....Pages 341-348
Remarks on the behaviour of flow of a three-dimensional perfect fluid in the presence of a small perturbation of the initial velocity field....Pages 349-355
The asymptotic Hopf invariant and its applications....Pages 357-375
A magnetic field in a moving conducting fluid....Pages 377-378
A magnetic field in a stationary flow with stretching in a Riemannian manifold fluid....Pages 379-382
Stationary magnetic field in a periodic flow fluid....Pages 383-385
Some remarks on the antidynamo theorem....Pages 387-396
Evolution of a magnetic field under the action of transfer and diffusion....Pages 397-398
The growth of a magnetic field in a three-dimensional steady incompressible flow....Pages 399-403
Evolution of a magnetic field under the action of drift and diffusion....Pages 405-418
Exponential scattering of trajectories and its hydrodynamical applications....Pages 419-427
Kolmogorov’s hydrodynamic attractors....Pages 429-432
Topological methods in hydrodynamics....Pages 433-454
Translator’s Preface to J. Milnor’s book ″Morse Theory″....Pages 455-456
Henri Poincaré: Selected Works in Three Volumes. Vol. I New Methods of Celestial Mechanics - Preface. From the editorial board. Comments....Pages 457-461
Comments on the paper “On a geometric theorem” by Henri Poincaré....Pages 463-464
Back Matter....Pages 465-465