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

• Main Authors: Franco Barragán, Alicia Santiago-Santos, Jesús F. Tenorio
• Format: Article
• Language: English
• Published: Universitat Politècnica de València 2020-04-01
• Series: Applied General Topology
• Subjects: 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
• Online Access: https://polipapers.upv.es/index.php/AGT/article/view/11807

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.