Crisis in chaotic scattering

Journal Article · Mon Oct 04 04:00:00 EDT 1993 · Physical Review Letters; (United States)

DOI:https://doi.org/10.1103/PhysRevLett.71.2212· OSTI ID:5920949

Lai, Y; Grebogi, C; Bluemel, R; Kan, I ^[1]

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1. Laboratory for Plasma Research; University of Maryland; College Park; Maryland 20742 (United States) Department of Biomedical Engineering; The Johns Hopkins University School of Medicine; Baltimore; Maryland 21205 (United States) Institute for Physical Science and Technology and Department of Mathematics; University of Maryland; College Park; Maryland 20742 (United States) Department of Physics and Astronomy; University of Delaware; Newark; Delaware 19716 (United States) Department of Mathematics; The George Mason University; Fairfax; Virginia 22030 (United States)

We show that in a chaotic scattering system the stable and unstable foliations of isolated chaotic invariant sets can become heteroclinically tangent to each other at an uncountably infinite number of parameter values. The first tangency, which is a crisis in chaotic scattering, provides the link between the chaotic sets. A striking consequence is that 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.

• OSTI ID: 5920949
• Journal Information: Physical Review Letters; (United States), Journal Name: Physical Review Letters; (United States) Vol. 71:14; ISSN 0031-9007; ISSN PRLTAO
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ATTRACTORS
DATA
ENERGY LOSSES
FRACTALS
HAMILTONIANS
INFORMATION
LOSSES
MATHEMATICAL OPERATORS
NUMERICAL DATA
ONE-DIMENSIONAL CALCULATIONS
QUANTUM OPERATORS
SCATTERING
SINGULARITY
THEORETICAL DATA
TRAJECTORIES