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Chaos on Fuzzy Dynamical Systems

Institut Universitari de Matemàtica Pura i Aplicada, Universitat Politècnica de València, 46022 València, Spain
Author to whom correspondence should be addressed.
Academic Editor: Michal Fečkan
Mathematics 2021, 9(20), 2629;
Received: 5 September 2021 / Revised: 6 October 2021 / Accepted: 11 October 2021 / Published: 18 October 2021
(This article belongs to the Special Issue Dynamical Systems and Their Applications Methods)
Given a continuous map f:XX on a metric space, it induces the maps f¯:K(X)K(X), on the hyperspace of nonempty compact subspaces of X, and f^: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¯), and (F(X),f^). 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 Jardón, Sánchez 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). View Full-Text
Keywords: chaotic operators; hypercyclic operators; hyperspaces of compact sets; spaces of fuzzy sets; A -transitivity chaotic operators; hypercyclic operators; hyperspaces of compact sets; spaces of fuzzy sets; A -transitivity
MDPI and ACS Style

Martínez-Giménez, F.; Peris, A.; Rodenas, F. Chaos on Fuzzy Dynamical Systems. Mathematics 2021, 9, 2629.

AMA Style

Martínez-Giménez F, Peris A, Rodenas F. Chaos on Fuzzy Dynamical Systems. Mathematics. 2021; 9(20):2629.

Chicago/Turabian Style

Martínez-Giménez, Félix, Alfred Peris, and Francisco Rodenas. 2021. "Chaos on Fuzzy Dynamical Systems" Mathematics 9, no. 20: 2629.

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