Dynamic properties for the induced maps in the symmetric products

José L. Gómez-Rueda, Alejandro Illanes and Héctor Méndez

Chaos, Solitons & Fractals, 2012, vol. 45, issue 9, 1180-1187

Abstract: For a metric continuum X, let Fn(X) be the hyperspace of nonempty subsets of X with at most n points. Given a map f:X→X we consider the induced map fn:Fn(X)→Fn(X) given by fn(A)=f(A) (the image of A under f). Given a dynamic property P, we study the implication: if A∈Fn(X) has property P in the system (Fn(X),fn), then each element of A has property P in the system (X,f), and we also study the converse implication. We consider properties as periodicity, recurrence, regular recurrence, etc.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:45:y:2012:i:9:p:1180-1187

DOI: 10.1016/j.chaos.2012.05.003

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