On a class of orbit closures with unique minimal sets
type: Item
instance of: scholarly article
title: On a class of orbit closures with unique minimal sets
zbMATH Open document ID: 0621.54026
author: B. George
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1986-01-01T00:00:00Z
review text: Let \(S=\{0,1\}\) and \(S^*=\cup_{k\geq 1}S^ k\) i.e. \(S^*\) is the set of all blocks in S. A map \(\theta\) : \({\mathbb{N}}\to S^*\) induces a map \({\bar \theta}\): \({\mathbb{N}}^{{\mathbb{Z}}}\to S^{{\mathbb{Z}}}\) once an origin is chosen. The paper deals with 0-1 sequences arising from the above construction when the image of \(\theta\) has infinitely many blocks. A class of such sequences whose orbit closures contain a unique minimal set is investigated. Necessary and sufficient conditions for unique ergodicity are obtained. It is also shown that the orbit closure is uniquely ergodic iff all its points are quasi-regular.
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 37A99
Mathematics Subject Classification ID: 28D05
zbMATH DE Number: 4007232
zbMATH Keywords: orbit closures
zbMATH Keywords: minimal set
zbMATH Keywords: ergodicity
MaRDI profile type: Publication
Recommended article: Q4952085
Recommended article: Uniqueness dictated by boundary orbit accumulation sets
Recommended article: A classification of orbits admitting a unique invariant measure
Recommended article: On almost periodic orbits and minimal sets
Recommended article: Orbit closures and invariants
Recommended article: A criterion on compactness of the set of bounded orbits
Recommended article: Q3788723
Recommended article: Q5691603
Recommended article: Minimal orbits of metrics
Recommended article: On closures of joint similarity orbits
description: scientific article; zbMATH DE number 4007232