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
Fil: Gómez, Ignacio Sebastián. Universidad Nacional de La Plata. Instituto de Física La Plata; Argentina.
Fil: Gómez, Ignacio Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Física La Plata; Argentina.
Fil: Gómez, Ignacio Sebastián. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentina.
Fil: Portesi, Mariela Adelina. Universidad Nacional de La Plata. Instituto de Física La Plata; Argentina.
Fil: Portesi, Mariela Adelina. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Física La Plata; Argentina.
Fil: Portesi, Mariela Adelina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentina.
Fil: Lamberti, Pedro Walter. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.
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.
info:eu-repo/semantics/publishedVersion
Fil: Gómez, Ignacio Sebastián. Universidad Nacional de La Plata. Instituto de Física La Plata; Argentina.
Fil: Gómez, Ignacio Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Física La Plata; Argentina.
Fil: Gómez, Ignacio Sebastián. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentina.
Fil: Portesi, Mariela Adelina. Universidad Nacional de La Plata. Instituto de Física La Plata; Argentina.
Fil: Portesi, Mariela Adelina. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Física La Plata; Argentina.
Fil: Portesi, Mariela Adelina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentina.
Fil: Lamberti, Pedro Walter. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.
Otras Ciencias Físicas
Fuente
e-ISSN: 1089-7682
ISSN: 1054-1500
Materia
Distinguishability
Statistical distance
Discrete maps
Nivel de accesibilidad
acceso abierto
Condiciones de uso
Repositorio
Repositorio Digital Universitario (UNC)
Institución
Universidad Nacional de Córdoba
OAI Identificador
oai:rdu.unc.edu.ar:11086/551747
Acceder
id RDUUNC_f4dbef38622d99b06d17683748c359bf
oai_identifier_str oai:rdu.unc.edu.ar:11086/551747
network_acronym_str RDUUNC
repository_id_str 2572
network_name_str Repositorio Digital Universitario (UNC)
spelling Distinguishability notion based on Wootters statistical distance : application to discrete mapsGómez, Ignacio SebastiánPortesi, Mariela AdelinaLamberti, Pedro WalterDistinguishabilityStatistical distanceDiscrete mapsFil: Gómez, Ignacio Sebastián. Universidad Nacional de La Plata. Instituto de Física La Plata; Argentina.Fil: Gómez, Ignacio Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Física La Plata; Argentina.Fil: Gómez, Ignacio Sebastián. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentina.Fil: Portesi, Mariela Adelina. Universidad Nacional de La Plata. Instituto de Física La Plata; Argentina.Fil: Portesi, Mariela Adelina. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Física La Plata; Argentina.Fil: Portesi, Mariela Adelina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentina.Fil: Lamberti, Pedro Walter. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.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.info:eu-repo/semantics/publishedVersionFil: Gómez, Ignacio Sebastián. Universidad Nacional de La Plata. Instituto de Física La Plata; Argentina.Fil: Gómez, Ignacio Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Física La Plata; Argentina.Fil: Gómez, Ignacio Sebastián. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentina.Fil: Portesi, Mariela Adelina. Universidad Nacional de La Plata. Instituto de Física La Plata; Argentina.Fil: Portesi, Mariela Adelina. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Física La Plata; Argentina.Fil: Portesi, Mariela Adelina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentina.Fil: Lamberti, Pedro Walter. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.Otras Ciencias Físicashttps://orcid.org/0000-0002-8212-5792https://orcid.org/0000-0002-3202-41252017info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/octet-streamGómez, I. S., Portesi, M. A. y Lamberti, P. W. (2017). Distinguishability notion based on Wootters statistical distance : application to discrete maps. Chaos: An Interdisciplinary Journal of Nonlinear Science, 27 (8), 083112. https://doi.org/10.1063/1.4998141http://hdl.handle.net/11086/551747https://doi.org/10.1063/1.4998141e-ISSN: 1089-7682ISSN: 1054-1500reponame:Repositorio Digital Universitario (UNC)instname:Universidad Nacional de Córdobainstacron:UNCenginfo:eu-repo/semantics/openAccess2025-09-29T13:42:40Zoai:rdu.unc.edu.ar:11086/551747Institucionalhttps://rdu.unc.edu.ar/Universidad públicaNo correspondehttp://rdu.unc.edu.ar/oai/snrdoca.unc@gmail.comArgentinaNo correspondeNo correspondeNo correspondeopendoar:25722025-09-29 13:42:41.165Repositorio Digital Universitario (UNC) - Universidad Nacional de Córdobafalse
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
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.contributor.none.fl_str_mv https://orcid.org/0000-0002-8212-5792
https://orcid.org/0000-0002-3202-4125
dc.subject.none.fl_str_mv Distinguishability
Statistical distance
Discrete maps
topic Distinguishability
Statistical distance
Discrete maps
dc.description.none.fl_txt_mv Fil: Gómez, Ignacio Sebastián. Universidad Nacional de La Plata. Instituto de Física La Plata; Argentina.
Fil: Gómez, Ignacio Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Física La Plata; Argentina.
Fil: Gómez, Ignacio Sebastián. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentina.
Fil: Portesi, Mariela Adelina. Universidad Nacional de La Plata. Instituto de Física La Plata; Argentina.
Fil: Portesi, Mariela Adelina. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Física La Plata; Argentina.
Fil: Portesi, Mariela Adelina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentina.
Fil: Lamberti, Pedro Walter. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.
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.
info:eu-repo/semantics/publishedVersion
Fil: Gómez, Ignacio Sebastián. Universidad Nacional de La Plata. Instituto de Física La Plata; Argentina.
Fil: Gómez, Ignacio Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Física La Plata; Argentina.
Fil: Gómez, Ignacio Sebastián. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentina.
Fil: Portesi, Mariela Adelina. Universidad Nacional de La Plata. Instituto de Física La Plata; Argentina.
Fil: Portesi, Mariela Adelina. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Física La Plata; Argentina.
Fil: Portesi, Mariela Adelina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentina.
Fil: Lamberti, Pedro Walter. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.
Otras Ciencias Físicas
description Fil: Gómez, Ignacio Sebastián. Universidad Nacional de La Plata. Instituto de Física La Plata; Argentina.
publishDate 2017
dc.date.none.fl_str_mv 2017
dc.type.none.fl_str_mv info:eu-repo/semantics/publishedVersion
info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
status_str publishedVersion
format article
dc.identifier.none.fl_str_mv Gómez, I. S., Portesi, M. A. y Lamberti, P. W. (2017). Distinguishability notion based on Wootters statistical distance : application to discrete maps. Chaos: An Interdisciplinary Journal of Nonlinear Science, 27 (8), 083112. https://doi.org/10.1063/1.4998141
http://hdl.handle.net/11086/551747
https://doi.org/10.1063/1.4998141
identifier_str_mv Gómez, I. S., Portesi, M. A. y Lamberti, P. W. (2017). Distinguishability notion based on Wootters statistical distance : application to discrete maps. Chaos: An Interdisciplinary Journal of Nonlinear Science, 27 (8), 083112. https://doi.org/10.1063/1.4998141
url http://hdl.handle.net/11086/551747
https://doi.org/10.1063/1.4998141
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/octet-stream
dc.source.none.fl_str_mv e-ISSN: 1089-7682
ISSN: 1054-1500
reponame:Repositorio Digital Universitario (UNC)
instname:Universidad Nacional de Córdoba
instacron:UNC
reponame_str Repositorio Digital Universitario (UNC)
collection Repositorio Digital Universitario (UNC)
instname_str Universidad Nacional de Córdoba
instacron_str UNC
institution UNC
repository.name.fl_str_mv Repositorio Digital Universitario (UNC) - Universidad Nacional de Córdoba
repository.mail.fl_str_mv oca.unc@gmail.com
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score 13.070432

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