Chapter 8. Regular and Irregular Motion in Conservative Systems

  1. Prof. Dr. H. G. Schuster1 and
  2. Lecturer Wolfram Just2

Published Online: 23 AUG 2005

DOI: 10.1002/3527604804.ch8

Deterministic Chaos: An Introduction, Fourth Edition

Deterministic Chaos: An Introduction, Fourth Edition

How to Cite

Schuster, H. G. and Just, W. (2005) Regular and Irregular Motion in Conservative Systems, in Deterministic Chaos: An Introduction, Fourth Edition, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, FRG. doi: 10.1002/3527604804.ch8

Author Information

  1. 1

    Christian Albrecht University Kiel, Department of Theoretical Physics, Germany

  2. 2

    Queen Mary/University of London, School of Mathematical Sciences, United Kingdom

Publication History

  1. Published Online: 23 AUG 2005
  2. Published Print: 26 JAN 2005

ISBN Information

Print ISBN: 9783527404155

Online ISBN: 9783527604807

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Keywords:

  • chaos;
  • deterministic chaos;
  • motion;
  • regular motion;
  • irregular motion;
  • conservative systems;
  • perturbation theory;
  • stable tori;
  • KAM theorem;
  • unstable tori;
  • Poincaré–Birkhoff theorem;
  • homoclinic points;
  • Arnold diffusion;
  • classical chaos;
  • ergodicity;
  • cat map

Summary

This chapter contains sections titled:

  • Coexistence of Regular and Irregular Motion

    • Integrable Systems

    • Perturbation Theory and Vanishing Denominators

    • Stable Tori and KAM Theorem

    • Unstable Tori and Poincaré–Birkhoff Theorem

    • Homoclinic Points and Chaos

    • Arnold Diffusion

    • Examples of Classical Chaos

  • Strongly Irregular Motion and Ergodicity

    • Cat Map

    • Hierarchy of Classical Chaos

    • Three Classical K-Systems