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

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Abstract: For minimal systems of zero topological entropy we demonstrate the sharp difference between the behavior, regarding entropy, of the systems and induced by on the spaces of probability measures on and of closed subsets of . It is shown that the system 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 and with respect to the existence of almost Hilbertian central sections of the unit ball. In contrast to this theorem we construct a minimal system of zero entropy with a minimal subsystem of whose entropy is positive.

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DOI:
https://doi.org/10.1090/S0894-0347-1995-1270579-5

Article copyright:
© Copyright 1995
American Mathematical Society