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Hydrodynamics, bifurcation theory, and algebraic geometry, 1965-1972

Author: V I Arnolʹd; Alexander Givental; Boris Khesin; A N Varchenko
Publisher: New York : Springer, [2013] ©2014
Series: Vladimir I. Arnold - collected works, 2
Edition/Format:   eBook : Document : English : First edition

Here is the second volume of the collected works of one of the great mathematical scientists of our time, renowned both for the breadth and depth of his work. This publication focuses on his research  Read more...


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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: V I Arnolʹd; Alexander Givental; Boris Khesin; A N Varchenko
ISBN: 9783642310317 3642310311 3642310303 9783642310300
OCLC Number: 868924560
Description: 1 online resource (458 pages).
Contents: 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 ecoulements 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 mathematiques de l'hydrodynamique et de la magnetohydrodynamique (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.
Series Title: Vladimir I. Arnold - collected works, 2
Responsibility: Vladimir I. Arnold ; [edited by] Alexander Givental, Boris Khesin, Alexander Varchenko.


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"Volume II focuses on hydrodynamics, bifurcation theory and algebraic geometry. ... Arnold was a very prolific writer. The publication of his collected works is a huge task and a great service to the Read more...

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