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Keywords = infinite-to-one

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10 pages, 274 KB  
Article
Fiber-Mixing Codes between Shifts of Finite Type and Factors of Gibbs Measures
by Uijin Jung
Entropy 2016, 18(12), 428; https://doi.org/10.3390/e18120428 - 30 Nov 2016
Cited by 2 | Viewed by 4148
Abstract
A sliding block code π : X Y between shift spaces is called fiber-mixing if, for every x and x in X with y = π ( x ) = π ( x ) , there is [...] Read more.
A sliding block code π : X Y between shift spaces is called fiber-mixing if, for every x and x in X with y = π ( x ) = π ( x ) , there is z π - 1 ( y ) which is left asymptotic to x and right asymptotic to x . 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. Full article
(This article belongs to the Special Issue Entropic Properties of Dynamical Systems)
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