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## Details

Genre/Form: | Electronic books Biography |
---|---|

Additional Physical Format: | Print version: Arnold, Vladimir I. Vladimir I. Arnold - Collected Works : Hydrodynamics, Bifurcation Theory, Algebraic Geometry, etc. 1965-1972. Dordrecht : Springer, ©2013 |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Vladimir I Arnold; Alexander Givental; Boris Khesin; Jerrold E Marsden; A N Varchenko; Victor A Vassiliev; Oleg Yanovich Viro; Vladimir Zakalyukin |

ISBN: | 9783642310317 3642310311 |

OCLC Number: | 866439747 |

Notes: | 34 A magnetic field in a stationary flow with stretching in a Riemannian manifold (with Ya. B. Zeldovich, A.A. Ruzmaikin, and D.D. Sokolov). |

Description: | 1 online resource (458 pages). |

Contents: | Preface; Acknowledgements; Contents; 1 A variational principle for three-dimensional steady flows of an ideal fluid; 2 On the Riemann curvature of diffeomorphism groups; 3 Sur la topologie des écoulements stationnaires des fluides parfaits (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 applications to the hydrodynamics of perfect fluids8 On a variational principle for the steady flows of perfect fluids and its applications to problems of non-linear stability; 9 On a characteristic class arising in quantization conditions; 10 A note on the Weierstrass preparation theorem; 11 The stability problem and ergodic properties for classical dynamical systems; 12 A remark on the ramification of hyperelliptic integrals as functions of parameters; 13 Singularities of smooth mappings. 14 Remarks on singularities of finite codimension in complex dynamical systems15 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 On the one-dimensional cohomology of the Lie algebra of divergence-free vector fields and rotation numbers of dynamical systems; 18 The cohomology ring of the colored braid group; 19 On cohomology classes of algebraic functions invariant under Tschirnhausen transformations; 20 Trivial problems; 21 Local problems of analysis. 22 Algebraic unsolvability of the problem of stability and the problem of topological classification of singular points of analytic systems of differential equations23 On some topological invariants of algebraic functions; 24 Topological invariants of algebraic functions II; 25 Algebraic unsolvability of the problem of Lyapunov stability and the problem of topological classification of singular points; 26 On the arrangement of ovals of real plane algebraic curves, involutions of four-dimensional smooth manifolds, and the arithmetic of integral quadratic forms. 27 The topology of real algebraic curves (works of I.G. Petrovsky and their development)28 On matrices depending on parameters; 29 Lectures on bifurcations in versal families; 30 Versal families and bifurcations of differential equations (Russian); 31 Remarks on the behaviour of a flow of a three-dimensional i fluid in the presence of a small perturbation of the initial vector field; 32 The asymptotic Hopf invariant and its applications; 33 A magnetic field in a moving conducting fluid (with Ya. B. Zeldovich, A.A. Ruzmaikin, and D.D. Sokolov). |

Series Title: | Vladimir I. Arnold - Collected Works. |

### Abstract:

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.

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