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
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/97900
Ver los metadatos del registro completo
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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) |
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openAccess |
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http://creativecommons.org/licenses/by-nc-sa/2.5/ar/ Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Argentina (CC BY-NC-SA 2.5) |
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