Chaos in the square billiard with a modified reflection law. (English) Zbl 1331.37051
Summary: 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.{
©2012 American Institute of Physics}
©2012 American Institute of Physics}
MSC:
37D50 | Hyperbolic systems with singularities (billiards, etc.) (MSC2010) |
37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
37D10 | Invariant manifold theory for dynamical systems |
37B40 | Topological entropy |
37B25 | Stability of topological dynamical systems |
37G15 | Bifurcations of limit cycles and periodic orbits in dynamical systems |
37J45 | Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010) |
37J15 | Symmetries, invariants, invariant manifolds, momentum maps, reduction (MSC2010) |
References:
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