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Markarian, R.; Rolla, L.T.; Sidoravicius, V.; Tal, F.A.; Vares, M.E. "Stochastic perturbations of convex billiards" (2015) Nonlinearity. 28(12):4425-4434
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Abstract:

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. © 2015 IOP Publishing Ltd & London Mathematical Society.

Registro:

Documento: Artículo
Título:Stochastic perturbations of convex billiards
Autor:Markarian, R.; Rolla, L.T.; Sidoravicius, V.; Tal, F.A.; Vares, M.E.
Filiación:IMERL, Facultad de Ingenieria, UdelaR, Avenida 18 de Julio 1968, Montevideo, 11200, Uruguay
Luis A. Santaló Mathematics Research Institute Conicet, UBA, Ciudad Universitaria, Buenos Aires, Argentina
IMPA, Estrada Dona Castorina, 110 - Jardim Botanico, Rio de Janeiro, RJ 22460-320, Brazil
Instituto de Matemática e Estatística, USP, Cidade Universitária, Rua do Matão 1010, São Paulo, SP 05508-090, Brazil
Instituto de Matemática, UFRJ, Av. Athos da Silveira Ramos 149, Rio de Janeiro, RJ 21941-901, Brazil
Palabras clave:Billiard systems; Invariant measure; Random perturbations; Uniform ergodicity
Año:2015
Volumen:28
Número:12
Página de inicio:4425
Página de fin:4434
DOI: http://dx.doi.org/10.1088/0951-7715/28/12/4425
Título revista:Nonlinearity
Título revista abreviado:Nonlinearity
ISSN:09517715
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09517715_v28_n12_p4425_Markarian

Referencias:

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Citas:

---------- APA ----------
Markarian, R., Rolla, L.T., Sidoravicius, V., Tal, F.A. & Vares, M.E. (2015) . Stochastic perturbations of convex billiards. Nonlinearity, 28(12), 4425-4434.
http://dx.doi.org/10.1088/0951-7715/28/12/4425
---------- CHICAGO ----------
Markarian, R., Rolla, L.T., Sidoravicius, V., Tal, F.A., Vares, M.E. "Stochastic perturbations of convex billiards" . Nonlinearity 28, no. 12 (2015) : 4425-4434.
http://dx.doi.org/10.1088/0951-7715/28/12/4425
---------- MLA ----------
Markarian, R., Rolla, L.T., Sidoravicius, V., Tal, F.A., Vares, M.E. "Stochastic perturbations of convex billiards" . Nonlinearity, vol. 28, no. 12, 2015, pp. 4425-4434.
http://dx.doi.org/10.1088/0951-7715/28/12/4425
---------- VANCOUVER ----------
Markarian, R., Rolla, L.T., Sidoravicius, V., Tal, F.A., Vares, M.E. Stochastic perturbations of convex billiards. Nonlinearity. 2015;28(12):4425-4434.
http://dx.doi.org/10.1088/0951-7715/28/12/4425