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

Fil: Gómez, Ignacio Sebastián. Universidad Nacional de La Plata. Instituto de Física La Plata; Argentina.

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Detalles Bibliográficos
Autores principales:	Gómez, Ignacio Sebastián, Portesi, Mariela Adelina, Lamberti, Pedro Walter
Otros Autores:	https://orcid.org/0000-0002-8212-5792
Formato:	publishedVersion article
Lenguaje:	Inglés
Publicado:	2024
Materias:	Distinguishability Statistical distance Discrete maps
Acceso en línea:	http://hdl.handle.net/11086/551747 https://doi.org/10.1063/1.4998141
Aporte de:	Repositorio Digital Universitario (UNC) de Universidad Nacional de Córdoba

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spelling	I10-R141-11086-5517472024-05-06T12:47:20Z Distinguishability notion based on Wootters statistical distance : application to discrete maps Gómez, Ignacio Sebastián Portesi, Mariela Adelina Lamberti, Pedro Walter https://orcid.org/0000-0002-8212-5792 https://orcid.org/0000-0002-3202-4125 Distinguishability Statistical distance Discrete maps 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. 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 2024-05-06T12:30:21Z 2024-05-06T12:30:21Z 2017 article 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 eng Atribución-NoComercial-SinDerivadas 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/deed.es Impreso; Electrónico y/o Digital e-ISSN: 1089-7682 ISSN: 1054-1500
institution	Universidad Nacional de Córdoba
institution_str	I-10
repository_str	R-141
collection	Repositorio Digital Universitario (UNC)
language	Inglés
topic	Distinguishability Statistical distance Discrete maps
spellingShingle	Distinguishability Statistical distance Discrete maps Gómez, Ignacio Sebastián Portesi, Mariela Adelina Lamberti, Pedro Walter Distinguishability notion based on Wootters statistical distance : application to discrete maps
topic_facet	Distinguishability Statistical distance Discrete maps
description	Fil: Gómez, Ignacio Sebastián. Universidad Nacional de La Plata. Instituto de Física La Plata; Argentina.
author2	https://orcid.org/0000-0002-8212-5792
author_facet	https://orcid.org/0000-0002-8212-5792 Gómez, Ignacio Sebastián Portesi, Mariela Adelina Lamberti, Pedro Walter
format	publishedVersion article
author	Gómez, Ignacio Sebastián Portesi, Mariela Adelina Lamberti, Pedro Walter
author_sort	Gómez, Ignacio Sebastián
title	Distinguishability notion based on Wootters statistical distance : application to 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
publishDate	2024
url	http://hdl.handle.net/11086/551747 https://doi.org/10.1063/1.4998141
work_keys_str_mv	AT gomezignaciosebastian distinguishabilitynotionbasedonwoottersstatisticaldistanceapplicationtodiscretemaps AT portesimarielaadelina distinguishabilitynotionbasedonwoottersstatisticaldistanceapplicationtodiscretemaps AT lambertipedrowalter distinguishabilitynotionbasedonwoottersstatisticaldistanceapplicationtodiscretemaps
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Distinguishability notion based on Wootters statistical distance : application to discrete maps

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