Dynamics of induced mappings on symmetric products, some answers
Submitted: 2022-04-08
|Accepted: 2022-05-18
|Published: 2022-10-03
Copyright (c) 2022 Applied General Topology
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
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Keywords:
continuum, dynamical system, induced mapping, irreducibility, symmetric product, turbulence
Supporting agencies:
PAPIIT
DGAPA
UNAM
CONACYT
Abstract:
Let X be a metric continuum and n a positive integer. Let Fn (X) be the hyperspace of nonempty subsets of X with at most n points. If 0 < m < n, we consider the quotient space Fnm (X) = Fn (X)/Fm (X). Given a mapping f from X into X, we consider the induced mappings fn from Fn (X) into Fn (X) and fnm from Fnm (X) into Fnm (X). In this paper we study the relations among the dynamics of the mappings f, fn, and fnm and we answer some questions, by F. Barragán, A. Santiago-Santos and J. Tenorio, related to the properties: minimality, irreducibility, strong transitive and turbulence.
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