Skip to main content
SpringerLink
Log in

Quasi-Periodic Motions in Families of Dynamical Systems

Order amidst Chaos

  • Book
  • © 1996

Overview

Authors:
  1. Hendrik W. Broer

    1. Department of Mathematics, University of Groningen, Groningen, The Netherlands

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. George B. Huitema

    1. KPN Research, Groningen, The Netherlands

    View author publications

    You can also search for this author in PubMed   Google Scholar

  3. Mikhail B. Sevryuk

    1. Institute of Energy Problems of Chemical Physics, Moscow, Russia

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1645)

  • 4254 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 69.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (6 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Introduction and examples

    Pages 1-40

  3. The conjugacy theory

    Pages 41-75

  4. The continuation theory

    Pages 77-82

  5. Complicated Whitney-smooth families

    Pages 83-121

  6. Conclusions

    Pages 123-139

  7. Appendices

    Pages 141-167

  8. Back Matter

    Pages 169-195
    Download chapter PDF
Back to top

Keywords

About this book

This book is devoted to the phenomenon of quasi-periodic motion in dynamical systems. Such a motion in the phase space densely fills up an invariant torus. This phenomenon is most familiar from Hamiltonian dynamics. Hamiltonian systems are well known for their use in modelling the dynamics related to frictionless mechanics, including the planetary and lunar motions. In this context the general picture appears to be as follows. On the one hand, Hamiltonian systems occur that are in complete order: these are the integrable systems where all motion is confined to invariant tori. On the other hand, systems exist that are entirely chaotic on each energy level. In between we know systems that, being sufficiently small perturbations of integrable ones, exhibit coexistence of order (invariant tori carrying quasi-periodic dynamics) and chaos (the so called stochastic layers). The Kolmogorov-Arnol'd-Moser (KAM) theory on quasi-periodic motions tells us that the occurrence of such motions is open within the class of all Hamiltonian systems: in other words, it is a phenomenon persistent under small Hamiltonian perturbations. Moreover, generally, for any such system the union of quasi-periodic tori in the phase space is a nowhere dense set of positive Lebesgue measure, a so called Cantor family. This fact implies that open classes of Hamiltonian systems exist that are not ergodic. The main aim of the book is to study the changes in this picture when other classes of systems - or contexts - are considered.

Authors and Affiliations

  • Department of Mathematics, University of Groningen, Groningen, The Netherlands

    Hendrik W. Broer

  • KPN Research, Groningen, The Netherlands

    George B. Huitema

  • Institute of Energy Problems of Chemical Physics, Moscow, Russia

    Mikhail B. Sevryuk

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation