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Almost minimal systems and periodicity in hyperspaces

Published online by Cambridge University Press:  14 March 2017

LEOBARDO FERNÁNDEZ ,
CHRIS GOOD  and
MATE PULJIZ Open the ORCID record for MATE PULJIZ [Opens in a new window]
LEOBARDO FERNÁNDEZ
Affiliation:
Facultad de Ciencias, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, México D.F., C.P. 04510, México email leobardof@ciencias.unam.mx
CHRIS GOOD
Affiliation:
School of Mathematics, University of Birmingham, Birmingham, B15 2TT, UK email c.good@bham.ac.uk, puljizmate@gmail.com
MATE PULJIZ
Affiliation:
School of Mathematics, University of Birmingham, Birmingham, B15 2TT, UK email c.good@bham.ac.uk, puljizmate@gmail.com
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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.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 6 , September 2018 , pp. 2158 - 2179
Copyright
© Cambridge University Press, 2017 

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