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Symmetric Chaos

  • Martin Golubitsky
  • Ian Stewart
Chapter
  • 691 Downloads
Part of the Progress in Mathematics book series (PM, volume 200)

Abstract

In nonlinear dynamics without symmetry there is a hierarchy of increasingly complicated dynamic behavior: steady-state, equilibrium, periodic, quasiperiodic, chaotic. See Ruelle and Takens [456] and Broeret al.[79]. So far we have studied analogous behavior for steady, periodic, and quasiperiodic states of equivariant differential equations, asking the following questions:
  • What symmetry groups, in principle, might states have?

  • What are the general existence and stability theorems?

  • what this book tries not to do

  • What is the interpretation in physical space of the symmetric dynamics found in phase space?

We now ask similar questions for chaotic solutions of equivariant dynamical systems.

Keywords

Invariant Measure Chaotic Attractor Isotropy Subgroup Ergodic Measure Chaotic Saddle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 2002

Authors and Affiliations

  • Martin Golubitsky
    • 1
  • Ian Stewart
    • 2
  1. 1.Department of MathematicsUniversity of HoustonHoustonUSA
  2. 2.Mathematics InstituteUniversity of WarwickCoventryUK

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