Dynamic properties of the dynamical system SFnm(X), SFnm(f))

Franco Barragán; Alicia Santiago-Santos; Jesús F. Tenorio

doi:10.4995/agt.2020.11807

Authors

Franco Barragán Universidad Tecnológica de la Mixteca
Alicia Santiago-Santos Universidad Tecnológica de la Mixteca
Jesús F. Tenorio Universidad Tecnológica de la Mixteca https://orcid.org/0000-0003-0705-3394

DOI:

https://doi.org/10.4995/agt.2020.11807

Keywords:

chaotic, continuum, dynamical system, exact, feebly open, hyperspace, induced map, irreducible, mixing, strongly transitive, symmetric product, symmetric product suspension, totally transitive, transitive, turbulent, weakly mixing

Abstract

Let X be a continuum and let n be a positive integer. We consider the hyperspaces F_n(X) and SF_n(X). If m is an integer such that n > m ≥ 1, we consider the quotient space SFⁿ_m(X). For a given map f : X â†’ X, we consider the induced maps F_n(f) : F_n(X) â†’ F_n(X), SF_n(f) : SF_n(X) â†’ SF_n(X) and SFⁿ_m(f) : SFⁿ_m(X) â†’ SFⁿ_m(X). In this paper, we introduce the dynamical system (SFⁿ_m(X), SFⁿ_m (f)) and we investigate some relationships between the dynamical systems (X, f), (F_n(X), F_n(f)), (SF_n(X), SF_n(f)) and (SFⁿ_m(X), SFⁿ_m(f)) when these systems are: exact, mixing, weakly mixing, transitive, totally transitive, strongly transitive, chaotic, irreducible, feebly open and turbulent.

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Author Biographies

Franco Barragán, Universidad Tecnológica de la Mixteca

Instituto de Física y Matemáticas

Alicia Santiago-Santos, Universidad Tecnológica de la Mixteca

Instituto de Física y Matemáticas

Jesús F. Tenorio, Universidad Tecnológica de la Mixteca

Instituto de Física y Matemáticas

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