Abrupt bifurcations in chaotic scattering: view from the anti-integrable limitDedicated to the memory of Leonid Pavlovich Shilnikov

Bleher, Ott and Grebogi found numerically an interesting chaotic phenomenon in 1989 for the scattering of a particle in a plane from a potential field with several peaks of equal height. They claimed that when the energy E of the particle is slightly less than the peak height Ec there is a hyperboli...

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Bibliographic Details
Published in:Nonlinearity 2013-08, Vol.26 (9), p.2703-2730
Main Authors: Baesens, Claude, Chen, Yi-Chiuan, MacKay, Robert S
Format: Article
Language:English
Subjects:
abrupt bifurcation
anti-integrable limit
chaotic scattering
Lagrangian system
topological Markov chain
Online Access:Get full text
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Summary:Bleher, Ott and Grebogi found numerically an interesting chaotic phenomenon in 1989 for the scattering of a particle in a plane from a potential field with several peaks of equal height. They claimed that when the energy E of the particle is slightly less than the peak height Ec there is a hyperbolic suspension of a topological Markov chain from which chaotic scattering occurs, whereas for E > Ec there are no bounded orbits. They called the bifurcation at E = Ec an abrupt bifurcation to chaotic scattering. The aim of this paper is to establish a rigorous mathematical explanation for how chaotic orbits occur via the bifurcation, from the viewpoint of the anti-integrable limit, and to do so for a general range of chaotic scattering problems.
ISSN:0951-7715
1361-6544
DOI:10.1088/0951-7715/26/9/2703