Browsing by Author "Pinheiro, Diogo"
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- Chaos in the square billiard with a modified reflection lawPublication . Del Magno, Gianluigi; Dias, João Lopes; Duarte, Pedro; Gaivão, José Pedro; Pinheiro, DiogoThe 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.
- Polygonal billiards with a contractive reflection law: a review of some hyperbolic propertiesPublication . Del Magno, Gianluigi; Dias, João Lopes; Duarte, Pedro; Gaivão, José Pedro; Pinheiro, DiogoWe provide an overview of recent results concerning the dynamics of polygonal billiards with a contractive reflection law.
- SRB measures for polygonal billiards with contracting reflection lawsPublication . Del Magno, Gianluigi; Dias, João Lopes; Duarte, Pedro; Gaivão, José Pedro; Pinheiro, DiogoWe prove that polygonal billiards with contracting reflection laws exhibit hyperbolic attractors with countably many ergodic SRB measures. These measures are robust under small perturbations of the reflection law, and the tables for which they exist form a generic set in the space of all convex polygons. Specific polygonal tables are studied in detail.