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Bifurcations of periodic and chaotic attractors in pinball billiards with focusing boundaries
| Citations: | 10 - 1 self |
BibTeX
@MISC{Arroyo_bifurcationsof,
author = {Aubin Arroyo and Roberto Markarian and David P. Sanders},
title = {Bifurcations of periodic and chaotic attractors in pinball billiards with focusing boundaries},
year = {}
}
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Abstract
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. Forall 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,Pujals and Sambarino [MPS08], we numerically investigate and characterise 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.
