Transition to chaotic scattering

Mingzhou Ding, Celso Grebogi, Edward Ott, James A. Yorke

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87 Citations (Scopus)

Abstract

This paper addresses the question of how chaotic scattering arises and evolves as a system parameter is continuously varied starting from a value for which the scattering is regular (i.e., not chaotic). Our results show that the transition from regular to chaotic scattering can occur via a saddle-center bifurcation, with further qualitative changes in the chaotic set resulting from a sequence of homoclinic and heteroclinic intersections. We also show that a state of "fully developed" chaotic scattering can be reached in our system through a process analogous to the formation of a Smale horseshoe. By fully developed chaotic scattering, we mean that the chaotic-invariant set is hyperbolic, and we find for our problem that all bounded orbits can be coded by a full shift on three symbols. Observable consequences related to qualitative changes in the chaotic set are also discussed.

Original languageEnglish
Pages (from-to)7025-7040
Number of pages16
JournalPhysical Review A
Volume42
Issue number12
DOIs
Publication statusPublished - 15 Dec 1990

Keywords

  • irregular scattering
  • potential scattering
  • vortex pairs
  • systems

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