Barragán, FrancoSantiago-Santos, AliciaTenorio, Jesús F.2020-04-272020-04-272020-04-031576-9402https://riunet.upv.es/handle/10251/141550[EN] 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.Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)ChaoticContinuumDynamical systemExactFeebly openHyperspaceInduced mapIrreducibleMixingStrongly transitiveSymmetric productSymmetric product suspensionTotally transitiveTransitiveTurbulentWeakly mixingArtículo10.4995/agt.2020.11807Abierto1989-4147