Vladimir I. Arnold - Collected Works by Arnold, Vladimir I.; Givental, Alexander B.; Khesin, Boris A.; Varchenko, Alexander N.; Vassiliev, Victor A.; Viro, Oleg Ya.; Auroux, Denis; Chenciner, Alain; Gould, Gerald G.;

Hydrodynamics, Bifurcation Theory, and Algebraic Geometry 1965-1972

Series: Vladimir I. Arnold - Collected Works; 2;

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Product details:

Edition number 2014
Publisher Springer Berlin Heidelberg
Date of Publication 30 December 2013
Number of Volumes 1 pieces, Book

ISBN 9783642310300
Binding Hardback
No. of pages465 pages
Size 244x170 mm
Weight 1002 g
Language English
Illustrations XIII, 465 p. 20 illus. Illustrations, black & white

Long description:

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.

"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 e?coulements 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 asfunctions 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 theuniverse.- 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 mathe?matiques de l'hydrodynamique et de la magne?tohydrodynamique (in English).- 47 Translator's Preface to J. Milnor's book ""Morse Theory"".- 48 Henri Poincare?: 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 Poincare?."