Universal minimal topological dynamical systems |
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Authors: | Ofek Shilon Benjamin Weiss |
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Institution: | (1) Simbionix Ltd., Hamelacha 6, Northern Industrial Zone, Lod, Israel, 71520;(2) Institute of Mathematics, Hebrew University of Jerusalem, Givat Ram, Jerusalem, 91904, Israel |
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Abstract: | Rokhlin (1963) showed that any aperiodic dynamical system with finite entropy admits a countable generating partition. Krieger
(1970) showed that aperiodic ergodic systems with entropy < log a, admit a generating partition with no more than a sets. In Symbolic Dynamics terminology, these results can be phrased— ℕℤ is a universal system in the category of aperiodic systems, and a]ℤ is a universal system for aperiodic ergodic systems with entropy < log a. Weiss (We89], 1989) presented a Minimal system, on a Compact space (a subshift of
) which is universal for aperiodic systems. In this work we present a joint generalization of both results: given ɛ, there
exists a minimal subshift of a]ℤ, universal for aperiodic ergodic systems with entropy < log a − ɛ. |
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