Chaos on Fuzzy Dynamical Systems

Félix Martínez-Giménez, Alfred Peris and Francisco Rodenas
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Félix Martínez-Giménez: Institut Universitari de Matemàtica Pura i Aplicada, Universitat Politècnica de València, 46022 València, Spain
Alfred Peris: Institut Universitari de Matemàtica Pura i Aplicada, Universitat Politècnica de València, 46022 València, Spain
Francisco Rodenas: Institut Universitari de Matemàtica Pura i Aplicada, Universitat Politècnica de València, 46022 València, Spain

Mathematics, 2021, vol. 9, issue 20, 1-11

Abstract: Given a continuous map f : X ? X 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).

Keywords: chaotic operators; hypercyclic operators; hyperspaces of compact sets; spaces of fuzzy sets; A -transitivity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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