Almost minimal systems and periodicity in hyperspaces

Leobardo Fernández, Christopher Good, Mate Puljiz

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
173 Downloads (Pure)

Abstract

Given a self-map of a compact metric space X, we study periodic points of the map induced on the hyperspace of closed non-empty subsets of X. We give some necessary conditions on admissible sets of periods for these maps. Seemingly unrelated to this, we construct an almost totally minimal homeomorphism of the Cantor set. We also apply our theory to give a full description of admissible period sets for induced maps of the interval maps. The description of admissible periods is also given for maps induced on symmetric products.
Original languageEnglish
Pages (from-to)2158-2179
Number of pages22
JournalErgodic Theory and Dynamical Systems
Volume38
Issue number6
Early online date14 Mar 2017
DOIs
Publication statusPublished - Sep 2018

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