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Abrupt bifurcations in chaotic scattering : view from the anti-integrable limit

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Baesens, Claude, Chen, Yi-Chiuan and MacKay, Robert S. (2013) Abrupt bifurcations in chaotic scattering : view from the anti-integrable limit. Nonlinearity, Volume 26 (Number 9). pp. 2703-2730. doi:10.1088/0951-7715/26/9/2703

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Official URL: http://dx.doi.org/10.1088/0951-7715/26/9/2703

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Abstract

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.

Item Type: Journal Article
Subjects: Q Science > QC Physics
Divisions: Faculty of Science > Physics
Library of Congress Subject Headings (LCSH): Chaotic behavior in systems
Journal or Publication Title: Nonlinearity
Publisher: Institute of Physics Publishing Ltd.
ISSN: 0951-7715
Official Date: September 2013
Dates:
DateEvent
September 2013Published
20 August 2013Available
Volume: Volume 26
Number: Number 9
Page Range: pp. 2703-2730
DOI: 10.1088/0951-7715/26/9/2703
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access
Funder: Guo jia ke xue wei yuan hui [National Science Council (Taiwan)]
Grant number: 99-2115-M-001-007 (NSC), 100-2115-M-001-007 (NSC), 101-2115-M-001-010 (NSC), EP/G021163/1 (EPSRC)

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