Stochastic perturbations of convex billiards

Autor(es)

Markarian, R. ^[1] ; Rolla, L. T. ^{[2, 3]} ; Sidoravicius, V. ^[4] ; Tal, F. A. ^[5] ; Vares, M. E. ^[6]

Afiliação do(s) autor(es)

^[1] IMERL, Fac Ingn, UdelaR, Montevideo 11200 - Uruguay

^[2] Consejo Nacl Invest Cient & Tecn, Luis A Santalo Math Res Inst, RA-1033 Buenos Aires, DF - Argentina

^[3] UBA, Buenos Aires, DF - Argentina

^[4] IMPA, BR-22460320 Rio De Janeiro, RJ - Brazil

^[5] Univ Sao Paulo, Inst Matemat & Estat, BR-05508090 Sao Paulo, SP - Brazil

^[6] Univ Fed Rio de Janeiro, Inst Matemat, BR-21941901 Rio De Janeiro, RJ - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Nonlinearity; v. 28, n. 12, p. 4425-4434, DEC 2015.
• Citações Web of Science: 1

Resumo

We consider a strictly convex billiard table with C-2 boundary, with the dynamics subjected to random perturbations. Each time the billiard ball hits the boundary its reflection angle has a random perturbation. The perturbation distribution corresponds to a situation where either the scale of the surface irregularities is smaller than but comparable to the diameter of the reflected object, or the billiard ball is not perfectly rigid. We prove that for a large class of such perturbations the resulting Markov chain is uniformly ergodic, although this is not true in general. (AU)

• Processo FAPESP: 11/16265-8 - Dinâmica em baixas dimensões
• Beneficiário: Edson Vargas
• Modalidade de apoio: Auxílio à Pesquisa - Temático