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.
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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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