Stochastic perturbations of convex billiards

Autores
Markarian, R.; Trivellato Rolla, Leonardo; Sidoravicius, V.; Tal, F. A.; Vares, M. E.
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
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 the physical 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.
Fil: Markarian, R.. Universidad de la Republica. Facultad de Ingeniería; Uruguay
Fil: Trivellato Rolla, Leonardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina
Fil: Sidoravicius, V.. Jardim Botânico; Brasil
Fil: Tal, F. A.. Universidade de Sao Paulo; Brasil
Fil: Vares, M. E.. Universidade Federal do Rio de Janeiro; Brasil
Materia
Billiard systems
Random perturbations
Uniform ergodicity
Invariant measure
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/18875
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Stochastic perturbations of convex billiardsMarkarian, R.Trivellato Rolla, LeonardoSidoravicius, V.Tal, F. A.Vares, M. E.Billiard systemsRandom perturbationsUniform ergodicityInvariant measurehttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We 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 the physical 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.Fil: Markarian, R.. Universidad de la Republica. Facultad de Ingeniería; UruguayFil: Trivellato Rolla, Leonardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; ArgentinaFil: Sidoravicius, V.. Jardim Botânico; BrasilFil: Tal, F. A.. Universidade de Sao Paulo; BrasilFil: Vares, M. E.. Universidade Federal do Rio de Janeiro; BrasilIOP Publishing2015-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/18875Markarian, R.; Trivellato Rolla, Leonardo; Sidoravicius, V.; Tal, F. A.; Vares, M. E.; Stochastic perturbations of convex billiards; IOP Publishing; Nonlinearity; 28; 12; 11-2015; 4425-44340951-7715CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1088/0951-7715/28/12/4425info:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/article/10.1088/0951-7715/28/12/4425/metainfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1409.5617info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:25:26Zoai:ri.conicet.gov.ar:11336/18875instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:25:26.868CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Stochastic perturbations of convex billiards
title Stochastic perturbations of convex billiards
spellingShingle Stochastic perturbations of convex billiards
Markarian, R.
Billiard systems
Random perturbations
Uniform ergodicity
Invariant measure
title_short Stochastic perturbations of convex billiards
title_full Stochastic perturbations of convex billiards
title_fullStr Stochastic perturbations of convex billiards
title_full_unstemmed Stochastic perturbations of convex billiards
title_sort Stochastic perturbations of convex billiards
dc.creator.none.fl_str_mv Markarian, R.
Trivellato Rolla, Leonardo
Sidoravicius, V.
Tal, F. A.
Vares, M. E.
author Markarian, R.
author_facet Markarian, R.
Trivellato Rolla, Leonardo
Sidoravicius, V.
Tal, F. A.
Vares, M. E.
author_role author
author2 Trivellato Rolla, Leonardo
Sidoravicius, V.
Tal, F. A.
Vares, M. E.
author2_role author
author
author
author
dc.subject.none.fl_str_mv Billiard systems
Random perturbations
Uniform ergodicity
Invariant measure
topic Billiard systems
Random perturbations
Uniform ergodicity
Invariant measure
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv 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 the physical 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.
Fil: Markarian, R.. Universidad de la Republica. Facultad de Ingeniería; Uruguay
Fil: Trivellato Rolla, Leonardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina
Fil: Sidoravicius, V.. Jardim Botânico; Brasil
Fil: Tal, F. A.. Universidade de Sao Paulo; Brasil
Fil: Vares, M. E.. Universidade Federal do Rio de Janeiro; Brasil
description 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 the physical 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.
publishDate 2015
dc.date.none.fl_str_mv 2015-11
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/18875
Markarian, R.; Trivellato Rolla, Leonardo; Sidoravicius, V.; Tal, F. A.; Vares, M. E.; Stochastic perturbations of convex billiards; IOP Publishing; Nonlinearity; 28; 12; 11-2015; 4425-4434
0951-7715
CONICET Digital
CONICET
url http://hdl.handle.net/11336/18875
identifier_str_mv Markarian, R.; Trivellato Rolla, Leonardo; Sidoravicius, V.; Tal, F. A.; Vares, M. E.; Stochastic perturbations of convex billiards; IOP Publishing; Nonlinearity; 28; 12; 11-2015; 4425-4434
0951-7715
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1088/0951-7715/28/12/4425
info:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/article/10.1088/0951-7715/28/12/4425/meta
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1409.5617
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv IOP Publishing
publisher.none.fl_str_mv IOP Publishing
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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