Minimal sets in compact connected subspaces
type: Item
instance of: scholarly article
title: Minimal sets in compact connected subspaces
zbMATH Open document ID: 1242.54018
published in: Topology and its Applications
publication date: 2011-10-10T00:00:00Z
review text: Consider a topological discrete dynamical system \((X,f)\), where \(X\) is a topological space and \(f: X\to X\) a continuous self-map. Let \(Y\subset X\) be a compact, connected and closed subset of \(X\). The objective of the present paper is to show that if the boundary \(\partial_XY\) contains exactly one point \(v\) and \(f(v)\in Y\), then \(Y\) contains a minimal set of \(f\).
reviewed by: Juan L. G. Guirao
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 37B05
Mathematics Subject Classification ID: 37B20
zbMATH DE Number: 5956071
zbMATH Keywords: topological space
zbMATH Keywords: continuous map
zbMATH Keywords: compactness
zbMATH Keywords: connectedness
zbMATH Keywords: minimal set
zbMATH Keywords: uniformly recurrent point
author: Jiehua Mai
MaRDI profile type: Publication
full work available at URL: j.topol.2011.06.059
OpenAlex ID: W1988021993
cites work: Q3660524
cites work: Q5557227
cites work: Dynamics in one dimension
cites work: A characterization of adding machine maps
cites work: Some remarks on almost periodic transformations
cites work: On almost periodic orbits and minimal sets
cites work: Strange triangular maps of the square
cites work: Almost periodic points and minimal sets in topological spaces
cites work: Orbit-closure decompositions and almost periodic properties
cites work: Almost periodic points with respect to transformation semi-groups
cites work: A characterization of zero topological entropy for a class of triangular mappings.
cites work: Recurrence in pairs
cites work: Simple Links and Fixed Sets Under Continuous Mappings
cites work: Q4233861
cites work: Proper minimal sets on compact connected 2-manifolds are nowhere dense
cites work: A note on almost periodic points and minimal sets in \(T_{1}\)- and \(T_{2}\)-spaces
cites work: Almost periodic points and minimal sets in \(\omega\)-regular spaces
cites work: Recurrent points and non-wandering points of graph maps
cites work: D-function of a minimal set and an extension of Sharkovskii's theorem to minimal sets
DOI: 10.1016/J.TOPOL.2011.06.059
description: scientific article; zbMATH DE number 5956071