Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A note on the existence of a largest topological factor with zero entropy


Authors: M. Lemanczyk and A. Siemaszko
Journal: Proc. Amer. Math. Soc. 129 (2001), 475-482
MSC (2000): Primary 37B40
DOI: https://doi.org/10.1090/S0002-9939-00-05892-5
Published electronically: July 27, 2000
MathSciNet review: 1800236
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract:

Given a topological system $T$ on a $\sigma$-compact Hausdorff space and its factor $S$ we show the existence of a largest topological factor $\hat{S}$ containing $S$ such that for each $\hat{S}$-invariant measure $\mu$, $h_\mu(\hat{S}\vert S)=0$. When a relative variational principle holds, $h(\hat{S})=h(S)$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 37B40

Retrieve articles in all journals with MSC (2000): 37B40


Additional Information

M. Lemanczyk
Affiliation: Faculty of Mathematics and Computer Science, Nicholas Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland
Email: mlem@mat.uni.torun.pl

A. Siemaszko
Affiliation: Department of Applied Mathematics, Olsztyn University of Agriculture and Technology, Oczapowskiego 1, 10-957 Olsztyn-Kortowo, Poland
Email: artur@art.olsztyn.pl

DOI: https://doi.org/10.1090/S0002-9939-00-05892-5
Keywords: Topological entropy, relative Pinsker factor
Received by editor(s): April 22, 1999
Published electronically: July 27, 2000
Communicated by: Michael Handel
Article copyright: © Copyright 2000 American Mathematical Society