Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics

Symmetries, Topology and Resonances in Hamiltonian Mechanics

Authors: Kozlov, Valerij V.

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About this book

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.

Table of contents (9 chapters)

  • Introduction

    Kozlov, Valerij V.

    Pages 1-9

  • Hamiltonian Mechanics

    Kozlov, Valerij V.

    Pages 11-54

  • Integration of Hamiltonian Systems

    Kozlov, Valerij V.

    Pages 55-124

  • Topological and Geometrical Obstructions to Complete Integrability

    Kozlov, Valerij V.

    Pages 125-147

  • Nonintegrability of Hamiltonian Systems Close to Integrable Ones

    Kozlov, Valerij V.

    Pages 148-221

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-642-78393-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $129.00
price for USA
  • ISBN 978-3-642-78395-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Symmetries, Topology and Resonances in Hamiltonian Mechanics
Authors
Translated by
Treshchev, D., Bolotin, S.V., Fedorov, Y.
Series Title
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Series Volume
31
Copyright
1996
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-78393-7
DOI
10.1007/978-3-642-78393-7
Softcover ISBN
978-3-642-78395-1
Series ISSN
0071-1136
Edition Number
1
Number of Pages
XI, 378
Additional Information
Original Russian edition published by Nauka
Topics