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Dynamical Systems VII

Integrable Systems Nonholonomic Dynamical Systems

  • Book
  • © 1994

Overview

Editors:
  1. V. I. Arnol’d
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  2. S. P. Novikov
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Part of the book series: Encyclopaedia of Mathematical Sciences (EMS, volume 16)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-vii
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  2. Nonholonomic Dynamical Systems, Geometry of Distributions and Variational Problems

    1. Front Matter

      Pages 1-3
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    2. Introduction

      • V. I. Arnol’d, S. P. Novikov
      Pages 4-9

    3. Geometry of Distributions

      • V. I. Arnol’d, S. P. Novikov
      Pages 10-35

    4. Basic Theory of Nonholonomic Riemannian Manifolds

      • V. I. Arnol’d, S. P. Novikov
      Pages 35-50

    5. Nonholonomic Variational Problems on Three-Dimensional Lie Groups

      • V. I. Arnol’d, S. P. Novikov
      Pages 51-81

  3. Integrable Systems II

    1. Front Matter

      Pages 83-86
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    2. Introduction

      • V. I. Arnol’d, S. P. Novikov
      Pages 86-86

    3. Integrable Systems and Finite-Dimensional Lie Algebras

      • M. A. Olshanetsky, A. M. Perelomov
      Pages 87-116

    4. Group-Theoretical Methods in the Theory of Finite-Dimensional Integrable Systems

      • A. G. Reyman, M. A. Semenov-Tian-Shansky
      Pages 116-225

    5. Quantization of Open Toda Lattices

      • M. A. Semenov-Tian-Shansky
      Pages 226-259

  4. Geometric and Algebraic Mechanisms of the Integrability of Hamiltonian Systems on Homogeneous Spaces and Lie Algebras

    1. Front Matter

      Pages 261-262
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    2. Geometry and Topology of Hamiltonian Systems

      • V. I. Arnol’d, S. P. Novikov
      Pages 263-303

    3. The Algebra of Hamiltonian Systems

      • V. I. Arnol’d, S. P. Novikov
      Pages 303-333

  5. Back Matter

    Pages 335-344
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