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

This document was uploaded by one of our users. The uploader already confirmed that they had the permission to publish it. If you are author/publisher or own the copyright of this documents, please report to us by using this DMCA report form.

Simply click on the Download Book button.

Yes, Book downloads on Ebookily are 100% Free.

Sometimes the book is free on Amazon As well, so go ahead and hit "Search on Amazon"

Vladimir Arnold was one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. At the same time he is one of the most prolific and outstanding mathematical authors. This second volume of his Collected Works focuses on hydrodynamics, bifurcation theory, and algebraic geometry.

Author(s): Vladimir I. Arnold (auth.), Alexander B. Givental, Boris A. Khesin, Alexander N. Varchenko, Victor A. Vassiliev, Oleg Ya. Viro (eds.)
Series: Vladimir I. Arnold - Collected Works 2
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2014

Language: English-Russian-French
Pages: 465
Tags: Mathematical Applications in the Physical Sciences; Algebraic Geometry; Mathematical Methods in Physics

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