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Chaos in the square billiard with a modified reflection law

2012; American Institute of Physics; Volume: 22; Issue: 2 Linguagem: Inglês

10.1063/1.3701992

1527-2443

Gianluigi Del Magno, João Lopes Dias, Pedro Duarte, José Pedro Gaivão, Diogo Pinheiro,

Chaos control and synchronization

The purpose of this paper is to study the dynamics of a square billiard with a non-standard reflection law such that the angle of reflection of the particle is a linear contraction of the angle of incidence. We present numerical and analytical arguments that the nonwandering set of this billiard decomposes into three invariant sets, a parabolic attractor, a chaotic attractor, and a set consisting of several horseshoes. This scenario implies the positivity of the topological entropy of the billiard, a property that is in sharp contrast with the integrability of the square billiard with the standard reflection law.