Remote Access Journal of the American Mathematical Society
Green Open Access

Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)

 
 

 

Quasi-factors of zero-entropy systems


Authors: Eli Glasner and Benjamin Weiss
Journal: J. Amer. Math. Soc. 8 (1995), 665-686
MSC: Primary 54H20; Secondary 28D20
DOI: https://doi.org/10.1090/S0894-0347-1995-1270579-5
MathSciNet review: 1270579
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For minimal systems $(X,T)$ of zero topological entropy we demonstrate the sharp difference between the behavior, regarding entropy, of the systems $(M(X),T)$ and $({2^X},T)$ induced by $T$ on the spaces $M(X)$ of probability measures on $X$ and ${2^X}$ of closed subsets of $X$. It is shown that the system $(M(X),T)$ has itself zero topological entropy. Two proofs of this theorem are given. The first uses ergodic theoretic ideas. The second relies on the different behavior of the Banach spaces $l_1^n$ and $l_\infty ^n$ with respect to the existence of almost Hilbertian central sections of the unit ball. In contrast to this theorem we construct a minimal system $(X,T)$ of zero entropy with a minimal subsystem $(Y,T)$ of $({2^X},T)$ whose entropy is positive.


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


Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC: 54H20, 28D20

Retrieve articles in all journals with MSC: 54H20, 28D20


Additional Information

Article copyright: © Copyright 1995 American Mathematical Society