Transition to Global Stochasticity

  • A. J. Lichtenberg
  • M. A. Lieberman
Part of the Applied Mathematical Sciences book series (AMS, volume 38)

Abstract

For near-integrable systems with two degrees of freedom, we have seen in Chapter 3 the existence of chaotic regions surrounding the separatrices associated with resonances. These regions persist for any nonzero perturbation strength ϵ, although their area tends to zero as ϵ → 0. Therefore, there is no abrupt “transition to stochasticity” at some critical ϵ, and one must define carefully the meaning of any such criterion.

Keywords

Rotation Number Primary Resonance Standard Mapping Continue Fraction Expansion Island Chain 
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 Science+Business Media New York 1992

Authors and Affiliations

  • A. J. Lichtenberg
    • 1
  • M. A. Lieberman
    • 1
  1. 1.Department of Electrical Engineering and Computer SciencesUniversity of CaliforniaBerkeleyUSA

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