Fiber-Mixing Codes between Shifts of Finite Type and Factors of Gibbs Measures
Department of Mathematics, Ajou University, 206 Worldcup-ro, Suwon 16499, Korea
Academic Editor: Tomasz Downarowicz
Received: 7 October 2016 / Revised: 20 November 2016 / Accepted: 24 November 2016 / Published: 30 November 2016
A sliding block code
between shift spaces is called fiber-mixing if, for every x
, there is
which is left asymptotic to x
and right asymptotic to
. A fiber-mixing factor code from a shift of finite type is a code of class degree 1 for which each point of Y
has exactly one transition class. Given an infinite-to-one factor code between mixing shifts of finite type (of unequal entropies), we show that there is also a fiber-mixing factor code between them. This result may be regarded as an infinite-to-one (unequal entropies) analogue of Ashley’s Replacement Theorem, which states that the existence of an equal entropy factor code between mixing shifts of finite type guarantees the existence of a degree 1 factor code between them. Properties of fiber-mixing codes and applications to factors of Gibbs measures are presented.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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MDPI and ACS Style
Jung, U. Fiber-Mixing Codes between Shifts of Finite Type and Factors of Gibbs Measures. Entropy 2016, 18, 428.
Jung U. Fiber-Mixing Codes between Shifts of Finite Type and Factors of Gibbs Measures. Entropy. 2016; 18(12):428.
Jung, Uijin. 2016. "Fiber-Mixing Codes between Shifts of Finite Type and Factors of Gibbs Measures." Entropy 18, no. 12: 428.
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