Chaos in the square billiard with a modified reflection law
  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. 
Gianluigi Del Magno, Jo\~ao Lopes Dias, Pedro Duarte, Jos\'e Pedro   Gaiv\~ao, Diogo Pinheiro
math.DS