Transition to chaotic scattering

Mingzhou Ding, Celso Grebogi, Edward Ott, and James A. Yorke
Phys. Rev. A 42, 7025 – Published 1 December 1990
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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 horse- shoe. 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.

  • Received 17 May 1990

DOI:https://doi.org/10.1103/PhysRevA.42.7025

©1990 American Physical Society

Authors & Affiliations

Mingzhou Ding

  • Laboratory for Plasma Research and Department of Physics, University of Maryland, College Park, Maryland 20742

Celso Grebogi

  • Laboratory for Plasma Research, Department of Mathematics, and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742

Edward Ott

  • Laboratory for Plasma Research, Department of Physics, and Department of Electrical Engineering, University of Maryland, College Park, Maryland 20742

James A. Yorke

  • Institute for Physical Science and Technology and Department of Mathematics, University of Maryland, College Park, Maryland 20742

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Vol. 42, Iss. 12 — December 1990

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