Dynamic properties of the dynamical system SFnm(X), SFnm(f))-Reference-Cited by-同舟云学术

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

Published:2020-04-03 Issue:1 Volume:21 Page:17
ISSN:1989-4147
Container-title:Applied General Topology
language:
Short-container-title:Appl. Gen. Topol.

Author:

Barragán Franco,Santiago-Santos Alicia,Tenorio Jesús F.^ORCID

Abstract

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

Publisher

Universitat Politecnica de Valencia

Subject

Geometry and Topology

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