Crisis and enhancement of chaotic scattering

Journal Article · Sun May 01 04:00:00 EDT 1994 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States)

DOI:https://doi.org/10.1103/PhysRevE.49.3761· OSTI ID:7206925

Lai, Y; Grebogi, C ^[1]

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1. Department of Biomedical Engineering, The Johns Hopkins University School of Medicine, Baltimore, Maryland 21205 (United States) Laboratory for Plasma Research, University of Maryland, College Park, Maryland 20742 (United States) Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742 (United States)

mChaotic scattering is characterized by the existence of nonattracting chaotic invariant sets in phase space. There can be several chaotic invariant sets coexisting in phase space when a system parameter value is below some critical value. As the parameter changes through the critical value, stable and unstable foliations of these chaotic invariant sets, which are fractal sets, can become tangent and then cross each other. The first tangency, which provides the linking between chaotic invariant sets, is a crisis in chaotic scattering. Above the crisis, there is an infinite number of such tangencies which keep occurring until the last tangency, above which the stable and unstable foliations cross transversely. As a consequence of this, the fractal dimension of the set of singularities in the scattering function increases in the parameter range determined by the first and the last tangencies. This leads to a proliferation of singularities in the scattering function and, consequently, to an enhancement of chaotic scattering. The phenomenon is investigated by using both simple one-dimensional models and a two-dimensional physical scattering system.

• OSTI ID: 7206925
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States), Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States) Vol. 49:5; ISSN 1063-651X; ISSN PLEEE8
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
AMPLITUDES
INVARIANCE PRINCIPLES
MATHEMATICAL SPACE
ONE-DIMENSIONAL CALCULATIONS
PHASE SPACE
RANDOMNESS
SCATTERING
SCATTERING AMPLITUDES
SINGULARITY
SPACE
STOCHASTIC PROCESSES
TWO-DIMENSIONAL CALCULATIONS