TY - JOUR

T1 - Quasi-factors of zero entropy systems

AU - Glasner, Eli

AU - Weiss, Benjamin

PY - 1995/7

Y1 - 1995/7

N2 - 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 (2X, T) induced by T on the spaces M(X) of probability measures on X and 2X 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 (Equation presented) and (Equation presented) 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 (2X, T) whose entropy is positive.

AB - 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 (2X, T) induced by T on the spaces M(X) of probability measures on X and 2X 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 (Equation presented) and (Equation presented) 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 (2X, T) whose entropy is positive.

UR - http://www.scopus.com/inward/record.url?scp=84967782933&partnerID=8YFLogxK

U2 - 10.1090/S0894-0347-1995-1270579-5

DO - 10.1090/S0894-0347-1995-1270579-5

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AN - SCOPUS:84967782933

SN - 0894-0347

VL - 8

SP - 665

EP - 686

JO - Journal of the American Mathematical Society

JF - Journal of the American Mathematical Society

IS - 3

ER -