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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
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: |
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| Date of first compliant deposit: | 27 December 2015 | ||||||
| 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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