Transition to chaotic scattering

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

Research output: Contribution to journalArticle

81 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

Cite this

Transition to chaotic scattering. / Ding, Mingzhou; Grebogi, Celso ; Ott, Edward; Yorke, James A.

In: Physical Review A, Vol. 42, No. 12, 15.12.1990, p. 7025-7040.

Research output: Contribution to journalArticle

Ding, M, Grebogi, C, Ott, E & Yorke, JA 1990, 'Transition to chaotic scattering', Physical Review A, vol. 42, no. 12, pp. 7025-7040. https://doi.org/10.1103/PhysRevA.42.7025
Ding, Mingzhou ; Grebogi, Celso ; Ott, Edward ; Yorke, James A. / Transition to chaotic scattering. In: Physical Review A. 1990 ; Vol. 42, No. 12. pp. 7025-7040.
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