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Preface

Published online by Cambridge University Press:  05 July 2011

Alfredo M. Ozorio de Almeida
Affiliation:
Universidade Estadual de Campinas, Brazil
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Summary

The discovery of chaotic behaviour in deterministic dynamical systems has had a profound effect in many areas of physics. There is now a large literature on this subject, which includes some important surveys. However, a physicist just entering this beautiful field or an advanced graduate student still finds the need for a concise introduction to the basic concepts in unsophisticated mathematical language. What are the essential distinctions between Hamiltonian (conservative) systems and dissipative systems? In what way will the presence of chaos in the classical limit affect a system appropriately described by quantum mechanics?

There is much to be gained by studying the theory of Hamiltonian systems against the background of general systems, in order to emphasize both contrasts and similarities. Liouville's theorem provides a remarkable distinguishing feature of Hamiltonian systems. The preservation of volume in phase space prevents the asymptotic collapse of the motion onto equilibria, periodic orbits, or ‘strange attractors’. Even though period-doubling cascades do occur in Hamiltonian systems, the loss of stability of a periodic orbit is only a local occurrence, rather than the-apocalyptic event that can subvert an entire dissipative system. In contrast the motion generated by a given Hamiltonian may exhibit diverse chaotic and regular orbits interwoven into rich structures.

Type
Chapter
Information
Hamiltonian Systems
Chaos and Quantization
, pp. vii - x
Publisher: Cambridge University Press
Print publication year: 1989

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  • Preface
  • Alfredo M. Ozorio de Almeida, Universidade Estadual de Campinas, Brazil
  • Book: Hamiltonian Systems
  • Online publication: 05 July 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511564161.001
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  • Preface
  • Alfredo M. Ozorio de Almeida, Universidade Estadual de Campinas, Brazil
  • Book: Hamiltonian Systems
  • Online publication: 05 July 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511564161.001
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Preface
  • Alfredo M. Ozorio de Almeida, Universidade Estadual de Campinas, Brazil
  • Book: Hamiltonian Systems
  • Online publication: 05 July 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511564161.001
Available formats
×