Chaos in the square billiard with a modified reflection law |
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Authors: | Del Magno Gianluigi Lopes Dias João Duarte Pedro Gaivão José Pedro Pinheiro Diogo |
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Institution: | CEMAPRE, ISEG, Universidade Te?cnica de Lisboa, Rua do Quelhas 6, 1200-781 Lisboa, Portugal. delmagno@iseg.utl.pt |
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Abstract: | 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. |
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