Dewey Class 
519 
Title 
Vladimir I. Arnold  Collected Works ([Ebook]) : Hydrodynamics, Bifurcation Theory, and Algebraic Geometry 19651972 / by Vladimir I. Arnold ; edited by Alexander B. Givental, Boris A. Khesin, Alexander N. Varchenko, Victor A. Vassiliev, Oleg Ya. Viro. 
Author 
Arnold, Vladimir Igorevic , 19372010 
Added Personal Name 
Givental, Alexander B. 
Khesin, Boris A. 
Varchenko, Alexander N. 
Vassiliev, Victor A. , 1956 
Viro, Oleg Ya 
Other name(s) 
SpringerLink (Online service) 
Publication 
Berlin, Heidelberg : Springer , 2014. 
Physical Details 
XIII, 465 pages:. 20 illus. : online resource. 
ISBN 
9783642310317 
Summary Note 
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.: 
Contents note 
1 Variational principle for threedimensional steadystate flows of an ideal fluid  2 On the Riemann curvature of diffeomorphism groups  3 Sur la topologie des écoulements stationnaires des fluides parfaits (in French)  4 Conditions for nonlinear stability of stationary plane curvilinear flows of an ideal fluid  5 On the topology of threedimensional steady flows of an ideal fluid  6 On an a priori estimate in the theory of hydrodynamical stability  7 On the differential geometry of infinitedimensional 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 nonlinear 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 Onedimensional cohomologies of the Lie algebras of nondivergence 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 fourdimensional smooth manifolds and the arithmetic of integer valued quadratic forms  29 Versal families and bifurcations of differential equations (in Russian)  30 Notes on the threedimensional 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 largescale structure of the universe I. General properties. One and twodimensional models  37 Elements of the largescale structure of the universe  38 Some remarks on the antidynamo theorem  39 Steadystate 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 threedimensional 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 mathématiques de l'hydrodynamique et de la magnétohydrodynamique (in English)  47 Translator's Preface to J. Milnor's book "Morse Theory"  48 Henri Poincaré: 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 Poincaré. 
System details note 
Online access is restricted to subscription institutions through IP address (only for SISSA internal users) 
Internet Site 
http://dx.doi.org/10.1007/9783642310317 
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