Ultrafilters and non-Cantor minimal sets in linearly ordered dynamical systems
type: Item
instance of: scholarly article
title: Ultrafilters and non-Cantor minimal sets in linearly ordered dynamical systems
zbMATH Open document ID: 1151.54031
published in: Archive for Mathematical Logic
publication date: 2008-08-18T00:00:00Z
full work available at URL: http://hdl.handle.net/10234/14153
review text: By a discrete dynamical system \((X,\varphi)\) is understood a continuous selfmap \(\varphi: X\to X\) of a Tychonoff space \(X\) into itself. A subset \(M\subseteq X\) is said to be minimal for \(\varphi\) if it is a minimal element in the set partially ordered by inclusion of all nonempty closed \(\varphi\)-invariant sets \(A\subseteq X\). As their main result the authors exhibit \(2^c\) nonhomeomorphic, nonmetrizable minimal sets in a compact connected linearly ordered dynamical system.
reviewed by: Ludvík Janoš
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 37E99
zbMATH DE Number: 5313045
zbMATH Keywords: dynamical system
zbMATH Keywords: minimal set
zbMATH Keywords: Cantor set
zbMATH Keywords: linearly ordered topological space
author: Michael Hrušák
author: Manuel Sanchis
author: Angel Tamariz-Mascarúa
MaRDI profile type: Publication
OpenAlex ID: W2160627392
cites work: Q3135846
cites work: A Note on Sarkovskiĭ's Theorem in Connected Linearly Ordered Spaces
cites work: Q3978759
cites work: Dynamics in one dimension
cites work: Q4150804
cites work: Q4376269
cites work: Q3744882
DOI: 10.1007/S00153-008-0069-3
description: scientific article; zbMATH DE number 5313045