Random interval homeomorphisms

We investigate homeomorphisms of a compact interval, applied randomly. We consider this system as a skew product with the two-sided Bernoulli shift in the base. If on the open interval there is a metric in which almost all maps are contractions, then (with mild additional assumptions) there exists a...

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Detalles Bibliográficos
Autores: Alsedà, Lluís|||0000-0001-9908-1063, Misiurewicz, Michal
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:150736
Acceso en línea:https://ddd.uab.cat/record/150736
https://dx.doi.org/urn:doi:10.5565/PUBLMAT_Extra14_01
Access Level:acceso abierto
Palabra clave:Attractors
Random system
Skew product
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spelling Random interval homeomorphismsAlsedà, Lluís|||0000-0001-9908-1063Misiurewicz, MichalAttractorsRandom systemSkew productWe investigate homeomorphisms of a compact interval, applied randomly. We consider this system as a skew product with the two-sided Bernoulli shift in the base. If on the open interval there is a metric in which almost all maps are contractions, then (with mild additional assumptions) there exists a global pullback attractor, which is a graph of a function from the base to the fiber. It is also a forward attractor. However, the value of this function depends only on the past, so when we take the one-sided shift in the base, it disappears. We illustrate those phenomena on an example, where there are two piecewise linear homeomorphisms, one moving points to the right and the other one to the left. 22014-01-0120142014-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/150736https://dx.doi.org/urn:doi:10.5565/PUBLMAT_Extra14_01reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2008-01486Ministerio de Educación y Ciencia MTM2011-26995-C02-01open accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:1507362026-06-06T12:50:31Z
dc.title.none.fl_str_mv Random interval homeomorphisms
title Random interval homeomorphisms
spellingShingle Random interval homeomorphisms
Alsedà, Lluís|||0000-0001-9908-1063
Attractors
Random system
Skew product
title_short Random interval homeomorphisms
title_full Random interval homeomorphisms
title_fullStr Random interval homeomorphisms
title_full_unstemmed Random interval homeomorphisms
title_sort Random interval homeomorphisms
dc.creator.none.fl_str_mv Alsedà, Lluís|||0000-0001-9908-1063
Misiurewicz, Michal
author Alsedà, Lluís|||0000-0001-9908-1063
author_facet Alsedà, Lluís|||0000-0001-9908-1063
Misiurewicz, Michal
author_role author
author2 Misiurewicz, Michal
author2_role author
dc.subject.none.fl_str_mv Attractors
Random system
Skew product
topic Attractors
Random system
Skew product
description We investigate homeomorphisms of a compact interval, applied randomly. We consider this system as a skew product with the two-sided Bernoulli shift in the base. If on the open interval there is a metric in which almost all maps are contractions, then (with mild additional assumptions) there exists a global pullback attractor, which is a graph of a function from the base to the fiber. It is also a forward attractor. However, the value of this function depends only on the past, so when we take the one-sided shift in the base, it disappears. We illustrate those phenomena on an example, where there are two piecewise linear homeomorphisms, one moving points to the right and the other one to the left.
publishDate 2014
dc.date.none.fl_str_mv 2
2014-01-01
2014
2014-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/150736
https://dx.doi.org/urn:doi:10.5565/PUBLMAT_Extra14_01
url https://ddd.uab.cat/record/150736
https://dx.doi.org/urn:doi:10.5565/PUBLMAT_Extra14_01
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2008-01486
Ministerio de Educación y Ciencia MTM2011-26995-C02-01
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
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