Measures and topological dynamics on Menger manifolds
type: Item
instance of: scholarly article
title: Measures and topological dynamics on Menger manifolds
zbMATH Open document ID: 0952.54020
DOI: 10.1016/S0166-8641(99)00009-7
published in: Topology and its Applications
publication date: 2001-01-10T00:00:00Z
review text: The authors study Menger manifolds from the viewpoint of dynamical systems. After some basic facts on Menger manifolds presented in the first section, in Section 2 the authors describe two ways to construct nonatomic, locally positive, Lebesgue-Stieltjes measures on compact Menger manifolds. Section 3 is devoted to the proof of the ``uniqueness'' of the Lebesgue-Stieltjes measure on any compact Menger manifold, next this result is applied in Section 4 to prove that the set of all ergodic homeomorphisms on any compact Menger manifold \(X\) forms a dense \(G_{\delta}\) set in the space of all measure preserving autohomeomorphisms of \(X\) with the compact-open topology. Finally, in Section 5 the authors prove the existence of homeomorphisms which are chaotic in the sense of Devaney as well as everywhere chaotic in the sense of Li-Yorke.
reviewed by: Neculai Papaghiuc
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 58C35
Mathematics Subject Classification ID: 37A99
Mathematics Subject Classification ID: 28C99
Mathematics Subject Classification ID: 57Q40
zbMATH DE Number: 1454825
zbMATH Keywords: Menger manifold
zbMATH Keywords: transitive homeomorphisms
zbMATH Keywords: ergodic homeomorphism
author: Hisao Kato
author: Kazuhiro Kawamura
author: H. M. Tuncali
author: E. D. Tymchatyn
MaRDI profile type: Publication
full work available at URL: s0166-8641(99)00009-7
OpenAlex ID: W2083181292
description: scientific article; zbMATH DE number 1454825