Vladimir I. Arnold - Collected Works

Hydrodynamics, Bifurcation Theory, and Algebraic Geometry 1965-1972

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ISBN: 978-3-642-31030-0 (Print) 978-3-642-31031-7 (Online)

Table of contents (45 chapters)

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  1. Front Matter

    Pages I-XIII

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    Book Chapter

    Pages 1-7

    A Variational principle for three-dimensional steady flows of an ideal fluid

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    Pages 9-13

    On the Riemann curvature of diffeomorphism groups

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    Pages 15-18

    Sur la topologie des écoulements stationnaires des fluides parfaits

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    Pages 19-23

    Conditions for non-linear stability of stationary plane curvilinear flows of an ideal fluid

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    Pages 25-28

    On the topology of three-dimensional steady flows of an ideal fluid

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    Pages 29-31

    On an a priori estimate in the theory of hydrodynamical stability

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    Pages 33-69

    On the differential geometry of infinite-dimensional Lie groups and its application to the hydrodynamics of perfect fluids

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    Pages 71-84

    On a variational principle for the steady flows of perfect fluids and its application to problems of non-linear stability

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    Pages 85-97

    On a characteristic class arising in quantization conditions

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    Pages 99-105

    A note on the Weierstrass preparation theorem

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    Pages 107-113

    The stability problem and ergodic properties for classical dynamical systems

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    Pages 115-118

    A remark on the ramification of hyperelliptic integrals as functions of parameters

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    Pages 119-161

    Singularities of smooth mappings

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    Pages 163-170

    Remarks on singularities of finite codimension in complex dynamical systems

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    Pages 171-173

    Braids of algebraic functions and the cohomology of swallowtails

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    Pages 175-178

    Hamiltonian nature of the Euler equations in the dynamics of a rigid body and of an ideal fluid

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    Pages 179-182

    On one-dimensional cohomology of the Lie algebra of divergence-free vector fields and on rotation numbers of dynamic systems

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    Pages 183-186

    The cohomology ring of the colored braid group

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    Pages 187-190

    On cohomology classes of algebraic functions invariant under Tschirnhausen transformations

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    Book Chapter

    Pages 191-191

    Trivial problems

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