Advertisement

Symmetries, Topology and Resonances in Hamiltonian Mechanics

  • Valerij V. Kozlov

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 31)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Valerij V. Kozlov
    Pages 1-9
  3. Valerij V. Kozlov
    Pages 11-54
  4. Valerij V. Kozlov
    Pages 55-124
  5. Valerij V. Kozlov
    Pages 222-275
  6. Valerij V. Kozlov
    Pages 337-366
  7. Back Matter
    Pages 367-380

About this book

Introduction

John Hornstein has written about the author's theorem on nonintegrability of geodesic flows on closed surfaces of genus greater than one: "Here is an example of how differential geometry, differential and algebraic topology, and Newton's laws make music together" (Amer. Math. Monthly, November 1989).
Kozlov's book is a systematic introduction to the problem of exact integration of equations of dynamics. The key to the solution is to find nontrivial symmetries of Hamiltonian systems. After Poincaré's work it became clear that topological considerations and the analysis of resonance phenomena play a crucial role in the problem on the existence of symmetry fields and nontrivial conservation laws.

Keywords

Bewegungsintegral Hamiltonian Mechanics Hamiltonsche Systeme Separatrixspaltung Symmetriefelder differential equation first integral invariant torus invarianter Torus splitting of separatrices symmetry field topology

Authors and affiliations

  • Valerij V. Kozlov
    • 1
  1. 1.Department of MathematicsMoscow State UniversityMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-78393-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 1996
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-78395-1
  • Online ISBN 978-3-642-78393-7
  • Series Print ISSN 0071-1136
  • Buy this book on publisher's site