Skip to Main Content

Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Quasi-factors of zero-entropy systems
HTML articles powered by AMS MathViewer

by Eli Glasner and Benjamin Weiss PDF
J. Amer. Math. Soc. 8 (1995), 665-686 Request permission

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
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
  • © Copyright 1995 American Mathematical Society
  • 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