Abstract:
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[EN] Given a continuous map f : X -> X on a metric space, it induces the maps f over bar :K(X) -> K(X), on the hyperspace of nonempty compact subspaces of X, and (f) over cap :F(X) -> F(X), on the space of normal fuzzy ...[+]
[EN] Given a continuous map f : X -> X on a metric space, it induces the maps f over bar :K(X) -> K(X), on the hyperspace of nonempty compact subspaces of X, and (f) over cap :F(X) -> F(X), on the space of normal fuzzy sets, consisting of the upper semicontinuous functions u:X -> [0,1] with compact support. Each of these spaces can be endowed with a respective metric. In this work, we studied the relationships among the dynamical systems (X,f), (K(X),f over bar ), and (F(X),(f) over cap). In particular, we considered several dynamical properties related to chaos: Devaney chaos, A-transitivity, Li-Yorke chaos, and distributional chaos, extending some results in work by Jardon, Sanchez and Sanchis (Mathematics 2020, 8, 1862) and work by Bernardes, Peris and Rodenas (Integr. Equ. Oper. Theory 2017, 88, 451-463). Especial attention is given to the dynamics of (continuous and linear) operators on metrizable topological vector spaces (linear dynamics).
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Project ID:
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info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-105011GB-I00/ES/DINAMICA DE OPERADORES/
info:eu-repo/grantAgreement/GENERALITAT VALENCIANA//PROMETEO%2F2017%2F102//ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y APLICACIONES./
info:eu-repo/grantAgreement/GENERALITAT VALENCIANA//PROMETEO%2F2021%2F070//Análisis funcional, dinámica de operadores y aplicaciones/
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Thanks:
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This work was supported by MCIN/AEI/10.13039/501100011033, Project PID2019-105011GB-I00, and by Generalitat Valenciana, Projects PROMETEO/2017/102 and PROMETEU/2021/070.
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