Abstract. Let X be a continuum. For any positive integer n we consider the hyperspace Fn(X) and if n is greater than or equal to two, we consider the quotient space SF n(X ) defined in [3]. For a given map f : X → X, we consider the induced maps Fn(f ) : Fn(X) → Fn(X) and SFn(f ) : SF n(X ) → SF n(X ) defined in [4]. Let M be one of the following classes of maps: exact, mixing, weakly mixing, transitive, totally transitive, strongly transitive, chaotic, minimal, irreducible, feebly open and turbulent. In this paper we study the relationships between the following statements: f ∈ M, Fn(f ) ∈ M and SF n(f ) ∈ M.
Abstract. We continue the work initiated by the first named author in Induced maps on n-fold symmetric product suspensions, Topology Appl. 158 (2011), 1192-1205. We consider classes of maps not included in the mentioned paper, namely: almost monotone, atriodic, freely decomposable, joining, monotonically refinable, refinable, semi-confluent, semi-open, simple and strongly freely decomposable maps.
<p>Let X be a continuum and let n be a positive integer. We consider the hyperspaces F<sub>n</sub>(X) and SF<sub>n</sub>(X). If m is an integer such that n > m ≥ 1, we consider the quotient space SF<sup>n</sup><sub>m</sub>(X). For a given map f : X → X, we consider the induced maps F<sub>n</sub>(f) : F<sub>n</sub>(X) → F<sub>n</sub>(X), SF<sub>n</sub>(f) : SF<sub>n</sub>(X) → SF<sub>n</sub>(X) and SF<sup>n</sup><sub>m</sub>(f) : SF<sup>n</sup><sub>m</sub>(X) → SF<sup>n</sup><sub>m</sub>(X). In this paper, we introduce the dynamical system (SF<sup>n</sup><sub>m</sub>(X), SF<sup>n</sup><sub>m</sub> (f)) and we investigate some relationships between the dynamical systems (X, f), (F<sub>n</sub>(X), F<sub>n</sub>(f)), (SF<sub>n</sub>(X), SF<sub>n</sub>(f)) and (SF<sup>n</sup><sub>m</sub>(X), SF<sup>n</sup><sub>m</sub>(f)) when these systems are: exact, mixing, weakly mixing, transitive, totally transitive, strongly transitive, chaotic, irreducible, feebly open and turbulent.</p>
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.