On α-Limit Sets in Lorenz Maps

The aim of this paper is to show that [Formula: see text]-limit sets in Lorenz maps do not have to be completely invariant. This highlights unexpected dynamical behavior in these maps, showing gaps existing in the literature. Similar result is obtained for unimodal maps on [Formula: see text]. On th...

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Detalles Bibliográficos
Autores principales: Cholewa, Łukasz, Oprocha, Piotr
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8469790/
https://www.ncbi.nlm.nih.gov/pubmed/34573778
http://dx.doi.org/10.3390/e23091153
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author Cholewa, Łukasz
Oprocha, Piotr
author_facet Cholewa, Łukasz
Oprocha, Piotr
author_sort Cholewa, Łukasz
collection PubMed
description The aim of this paper is to show that [Formula: see text]-limit sets in Lorenz maps do not have to be completely invariant. This highlights unexpected dynamical behavior in these maps, showing gaps existing in the literature. Similar result is obtained for unimodal maps on [Formula: see text]. On the basis of provided examples, we also present how the performed study on the structure of [Formula: see text]-limit sets is closely connected with the calculation of the topological entropy.
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spelling pubmed-84697902021-09-27 On α-Limit Sets in Lorenz Maps Cholewa, Łukasz Oprocha, Piotr Entropy (Basel) Article The aim of this paper is to show that [Formula: see text]-limit sets in Lorenz maps do not have to be completely invariant. This highlights unexpected dynamical behavior in these maps, showing gaps existing in the literature. Similar result is obtained for unimodal maps on [Formula: see text]. On the basis of provided examples, we also present how the performed study on the structure of [Formula: see text]-limit sets is closely connected with the calculation of the topological entropy. MDPI 2021-09-02 /pmc/articles/PMC8469790/ /pubmed/34573778 http://dx.doi.org/10.3390/e23091153 Text en © 2021 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Cholewa, Łukasz
Oprocha, Piotr
On α-Limit Sets in Lorenz Maps
title On α-Limit Sets in Lorenz Maps
title_full On α-Limit Sets in Lorenz Maps
title_fullStr On α-Limit Sets in Lorenz Maps
title_full_unstemmed On α-Limit Sets in Lorenz Maps
title_short On α-Limit Sets in Lorenz Maps
title_sort on α-limit sets in lorenz maps
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8469790/
https://www.ncbi.nlm.nih.gov/pubmed/34573778
http://dx.doi.org/10.3390/e23091153
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