English

Chaos in the square billiard with a modified reflection law

Dynamical Systems 2015-06-03 v2

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.

Keywords

Cite

@article{arxiv.1112.1753,
  title  = {Chaos in the square billiard with a modified reflection law},
  author = {Gianluigi Del Magno and João Lopes Dias and Pedro Duarte and José Pedro Gaivão and Diogo Pinheiro},
  journal= {arXiv preprint arXiv:1112.1753},
  year   = {2015}
}

Comments

17 figures

R2 v1 2026-06-21T19:48:10.724Z