Orbits of homogeneous polynomials on Banach spaces

Autores
Cardeccia, Rodrigo Alejandro; Muro, Luis Santiago Miguel
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the dynamics induced by homogeneous polynomials on Banach spaces. It is known that no homogeneous polynomial defined on a Banach space can have a dense orbit. We show a simple and natural example of a homogeneous polynomial with an orbit that is at the same time-dense (the orbit meets every ball of radius), weakly dense and such that is dense for every that either is unbounded or has 0 as an accumulation point. Moreover, we generalize the construction to arbitrary infinite-dimensional separable Banach spaces. To prove this, we study Julia sets of homogeneous polynomials on Banach spaces.
Fil: Cardeccia, Rodrigo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Muro, Luis Santiago Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; Argentina
Materia
HYPERCYCLIC OPERATORS
JULIA SETS
POLYNOMICAL DYNAMICS
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:11336/141629
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Orbits of homogeneous polynomials on Banach spacesCardeccia, Rodrigo AlejandroMuro, Luis Santiago MiguelHYPERCYCLIC OPERATORSJULIA SETSPOLYNOMICAL DYNAMICShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the dynamics induced by homogeneous polynomials on Banach spaces. It is known that no homogeneous polynomial defined on a Banach space can have a dense orbit. We show a simple and natural example of a homogeneous polynomial with an orbit that is at the same time-dense (the orbit meets every ball of radius), weakly dense and such that is dense for every that either is unbounded or has 0 as an accumulation point. Moreover, we generalize the construction to arbitrary infinite-dimensional separable Banach spaces. To prove this, we study Julia sets of homogeneous polynomials on Banach spaces.Fil: Cardeccia, Rodrigo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Muro, Luis Santiago Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; ArgentinaCambridge University Press2021-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/141629Cardeccia, Rodrigo Alejandro; Muro, Luis Santiago Miguel; Orbits of homogeneous polynomials on Banach spaces; Cambridge University Press; Ergodic Theory And Dynamical Systems; 41; 6; 6-2021; 1627-16550143-3857CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/abs/orbits-of-homogeneous-polynomials-on-banach-spaces/13760F4715E433F6390CE6D84F956E36info:eu-repo/semantics/altIdentifier/doi/10.1017/etds.2020.17info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1806.11543info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:03:30Zoai:ri.conicet.gov.ar:11336/141629instacron: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:34982025-09-03 10:03:30.419CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Orbits of homogeneous polynomials on Banach spaces
title Orbits of homogeneous polynomials on Banach spaces
spellingShingle Orbits of homogeneous polynomials on Banach spaces
Cardeccia, Rodrigo Alejandro
HYPERCYCLIC OPERATORS
JULIA SETS
POLYNOMICAL DYNAMICS
title_short Orbits of homogeneous polynomials on Banach spaces
title_full Orbits of homogeneous polynomials on Banach spaces
title_fullStr Orbits of homogeneous polynomials on Banach spaces
title_full_unstemmed Orbits of homogeneous polynomials on Banach spaces
title_sort Orbits of homogeneous polynomials on Banach spaces
dc.creator.none.fl_str_mv Cardeccia, Rodrigo Alejandro
Muro, Luis Santiago Miguel
author Cardeccia, Rodrigo Alejandro
author_facet Cardeccia, Rodrigo Alejandro
Muro, Luis Santiago Miguel
author_role author
author2 Muro, Luis Santiago Miguel
author2_role author
dc.subject.none.fl_str_mv HYPERCYCLIC OPERATORS
JULIA SETS
POLYNOMICAL DYNAMICS
topic HYPERCYCLIC OPERATORS
JULIA SETS
POLYNOMICAL DYNAMICS
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 study the dynamics induced by homogeneous polynomials on Banach spaces. It is known that no homogeneous polynomial defined on a Banach space can have a dense orbit. We show a simple and natural example of a homogeneous polynomial with an orbit that is at the same time-dense (the orbit meets every ball of radius), weakly dense and such that is dense for every that either is unbounded or has 0 as an accumulation point. Moreover, we generalize the construction to arbitrary infinite-dimensional separable Banach spaces. To prove this, we study Julia sets of homogeneous polynomials on Banach spaces.
Fil: Cardeccia, Rodrigo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Muro, Luis Santiago Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; Argentina
description We study the dynamics induced by homogeneous polynomials on Banach spaces. It is known that no homogeneous polynomial defined on a Banach space can have a dense orbit. We show a simple and natural example of a homogeneous polynomial with an orbit that is at the same time-dense (the orbit meets every ball of radius), weakly dense and such that is dense for every that either is unbounded or has 0 as an accumulation point. Moreover, we generalize the construction to arbitrary infinite-dimensional separable Banach spaces. To prove this, we study Julia sets of homogeneous polynomials on Banach spaces.
publishDate 2021
dc.date.none.fl_str_mv 2021-06
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/11336/141629
Cardeccia, Rodrigo Alejandro; Muro, Luis Santiago Miguel; Orbits of homogeneous polynomials on Banach spaces; Cambridge University Press; Ergodic Theory And Dynamical Systems; 41; 6; 6-2021; 1627-1655
0143-3857
CONICET Digital
CONICET
url http://hdl.handle.net/11336/141629
identifier_str_mv Cardeccia, Rodrigo Alejandro; Muro, Luis Santiago Miguel; Orbits of homogeneous polynomials on Banach spaces; Cambridge University Press; Ergodic Theory And Dynamical Systems; 41; 6; 6-2021; 1627-1655
0143-3857
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/abs/orbits-of-homogeneous-polynomials-on-banach-spaces/13760F4715E433F6390CE6D84F956E36
info:eu-repo/semantics/altIdentifier/doi/10.1017/etds.2020.17
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1806.11543
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
application/pdf
dc.publisher.none.fl_str_mv Cambridge University Press
publisher.none.fl_str_mv Cambridge University Press
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 13.13397

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