Distinguishability notion based on Wootters statistical distance : Application to discrete maps

Autores
Gómez, Ignacio Sebastián; Portesi, Mariela Adelina; Lamberti, Pedro Walter
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the distinguishability notion given by Wootters for states represented by probability density functions. This presents the particularity that it can also be used for defining a statistical distance in chaotic unidimensional maps. Based on that definition, we provide a metric d for an arbitrary discrete map. Moreover, from d, we associate a metric space with each invariant density of a given map, which results to be the set of all distinguished points when the number of iterations of the map tends to infinity. Also, we give a characterization of the wandering set of a map in terms of the metric d, which allows us to identify the dissipative regions in the phase space. We illustrate the results in the case of the logistic and the circle maps numerically and analytically, and we obtain d and the wandering set for some characteristic values of their parameters. Finally, an extension of the metric space associated for arbitrary probability distributions (not necessarily invariant densities) is given along with some consequences. The statistical properties of distributions given by histograms are characterized in terms of the cardinal of the associated metric space. For two conjugate variables, the uncertainty principle is expressed in terms of the diameters of the associated metric space with those variables.
Instituto de Física La Plata
Materia
Astronomía
Física
Distinguishability
Statistical distance
Discrete maps
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/97900

id SEDICI_7dc5c95e398794f0a7129cfe3a1f45b6
oai_identifier_str oai:sedici.unlp.edu.ar:10915/97900
network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling Distinguishability notion based on Wootters statistical distance : Application to discrete mapsGómez, Ignacio SebastiánPortesi, Mariela AdelinaLamberti, Pedro WalterAstronomíaFísicaDistinguishabilityStatistical distanceDiscrete mapsWe study the distinguishability notion given by Wootters for states represented by probability density functions. This presents the particularity that it can also be used for defining a statistical distance in chaotic unidimensional maps. Based on that definition, we provide a metric d for an arbitrary discrete map. Moreover, from d, we associate a metric space with each invariant density of a given map, which results to be the set of all distinguished points when the number of iterations of the map tends to infinity. Also, we give a characterization of the wandering set of a map in terms of the metric d, which allows us to identify the dissipative regions in the phase space. We illustrate the results in the case of the logistic and the circle maps numerically and analytically, and we obtain d and the wandering set for some characteristic values of their parameters. Finally, an extension of the metric space associated for arbitrary probability distributions (not necessarily invariant densities) is given along with some consequences. The statistical properties of distributions given by histograms are characterized in terms of the cardinal of the associated metric space. For two conjugate variables, the uncertainty principle is expressed in terms of the diameters of the associated metric space with those variables.Instituto de Física La Plata2017info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://sedici.unlp.edu.ar/handle/10915/97900enginfo:eu-repo/semantics/altIdentifier/url/https://ri.conicet.gov.ar/11336/65842info:eu-repo/semantics/altIdentifier/url/https://aip.scitation.org/doi/10.1063/1.4998141info:eu-repo/semantics/altIdentifier/issn/1089-7682info:eu-repo/semantics/altIdentifier/doi/10.1063/1.4998141info:eu-repo/semantics/altIdentifier/hdl/11336/65842info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/2.5/ar/Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Argentina (CC BY-NC-SA 2.5)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T11:20:20Zoai:sedici.unlp.edu.ar:10915/97900Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:20:21.024SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Distinguishability notion based on Wootters statistical distance : Application to discrete maps
title Distinguishability notion based on Wootters statistical distance : Application to discrete maps
spellingShingle Distinguishability notion based on Wootters statistical distance : Application to discrete maps
Gómez, Ignacio Sebastián
Astronomía
Física
Distinguishability
Statistical distance
Discrete maps
title_short Distinguishability notion based on Wootters statistical distance : Application to discrete maps
title_full Distinguishability notion based on Wootters statistical distance : Application to discrete maps
title_fullStr Distinguishability notion based on Wootters statistical distance : Application to discrete maps
title_full_unstemmed Distinguishability notion based on Wootters statistical distance : Application to discrete maps
title_sort Distinguishability notion based on Wootters statistical distance : Application to discrete maps
dc.creator.none.fl_str_mv Gómez, Ignacio Sebastián
Portesi, Mariela Adelina
Lamberti, Pedro Walter
author Gómez, Ignacio Sebastián
author_facet Gómez, Ignacio Sebastián
Portesi, Mariela Adelina
Lamberti, Pedro Walter
author_role author
author2 Portesi, Mariela Adelina
Lamberti, Pedro Walter
author2_role author
author
dc.subject.none.fl_str_mv Astronomía
Física
Distinguishability
Statistical distance
Discrete maps
topic Astronomía
Física
Distinguishability
Statistical distance
Discrete maps
dc.description.none.fl_txt_mv We study the distinguishability notion given by Wootters for states represented by probability density functions. This presents the particularity that it can also be used for defining a statistical distance in chaotic unidimensional maps. Based on that definition, we provide a metric d for an arbitrary discrete map. Moreover, from d, we associate a metric space with each invariant density of a given map, which results to be the set of all distinguished points when the number of iterations of the map tends to infinity. Also, we give a characterization of the wandering set of a map in terms of the metric d, which allows us to identify the dissipative regions in the phase space. We illustrate the results in the case of the logistic and the circle maps numerically and analytically, and we obtain d and the wandering set for some characteristic values of their parameters. Finally, an extension of the metric space associated for arbitrary probability distributions (not necessarily invariant densities) is given along with some consequences. The statistical properties of distributions given by histograms are characterized in terms of the cardinal of the associated metric space. For two conjugate variables, the uncertainty principle is expressed in terms of the diameters of the associated metric space with those variables.
Instituto de Física La Plata
description We study the distinguishability notion given by Wootters for states represented by probability density functions. This presents the particularity that it can also be used for defining a statistical distance in chaotic unidimensional maps. Based on that definition, we provide a metric d for an arbitrary discrete map. Moreover, from d, we associate a metric space with each invariant density of a given map, which results to be the set of all distinguished points when the number of iterations of the map tends to infinity. Also, we give a characterization of the wandering set of a map in terms of the metric d, which allows us to identify the dissipative regions in the phase space. We illustrate the results in the case of the logistic and the circle maps numerically and analytically, and we obtain d and the wandering set for some characteristic values of their parameters. Finally, an extension of the metric space associated for arbitrary probability distributions (not necessarily invariant densities) is given along with some consequences. The statistical properties of distributions given by histograms are characterized in terms of the cardinal of the associated metric space. For two conjugate variables, the uncertainty principle is expressed in terms of the diameters of the associated metric space with those variables.
publishDate 2017
dc.date.none.fl_str_mv 2017
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
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://sedici.unlp.edu.ar/handle/10915/97900
url http://sedici.unlp.edu.ar/handle/10915/97900
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://ri.conicet.gov.ar/11336/65842
info:eu-repo/semantics/altIdentifier/url/https://aip.scitation.org/doi/10.1063/1.4998141
info:eu-repo/semantics/altIdentifier/issn/1089-7682
info:eu-repo/semantics/altIdentifier/doi/10.1063/1.4998141
info:eu-repo/semantics/altIdentifier/hdl/11336/65842
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Argentina (CC BY-NC-SA 2.5)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Argentina (CC BY-NC-SA 2.5)
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
_version_ 1844616077490782208
score 13.070432