Aubin Arroyo et al 2009 Nonlinearity 22 1499 doi:10.1088/0951-7715/22/7/001
Bifurcations of periodic and chaotic attractors in pinball billiards with focusing boundaries
Aubin Arroyo1, Roberto Markarian2 and David P Sanders3
Show affiliationsRecommended by C P Dettmann
We study the dynamics of billiard models with a modified collision rule: the outgoing angle from a collision is a uniform contraction, by a factor λ, of the incident angle. These pinball billiards interpolate between a one-dimensional map when λ = 0 and the classical Hamiltonian case of elastic collisions when λ = 1. For all λ < 1, the dynamics is dissipative, and thus gives rise to attractors, which may be periodic or chaotic. Motivated by recent rigorous results of Markarian et al (http://premat.fing.edu.uy/papers/2008/110.pdf and http://www.preprint.impa.br/Shadows/SERIE_A/2008/614.html), we numerically investigate and characterize the bifurcations of the resulting attractors as the contraction parameter is varied. Some billiards exhibit only periodic attractors, some only chaotic attractors and others have coexistence of the two types.
- PACS
- MSC
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37D50 Hyperbolic systems with singularities (billiards, etc.)
58J55 Bifurcation (See also 35B32)
- Subjects
- Dates
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Issue 7 (July 2009)
Received 4 February 2009, in final form 24 April 2009
Published 28 May 2009
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Bifurcations of periodic and chaotic attractors in pinball billiards with focusing boundaries
Aubin Arroyo et al 2009 Nonlinearity 22 1499
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