{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:20:22Z","timestamp":1760242822770,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2016,11,30]],"date-time":"2016-11-30T00:00:00Z","timestamp":1480464000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A sliding block code     \u03c0 : X \u2192 Y     between shift spaces is called fiber-mixing if, for every x and     x \u2032     in X with     y = \u03c0  ( x )  = \u03c0  (  x \u2032  )     , there is     z \u2208  \u03c0  - 1    ( y )      which is left asymptotic to x and right asymptotic to     x \u2032    . 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\u2019s 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.<\/jats:p>","DOI":"10.3390\/e18120428","type":"journal-article","created":{"date-parts":[[2016,11,30]],"date-time":"2016-11-30T10:10:36Z","timestamp":1480500636000},"page":"428","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Fiber-Mixing Codes between Shifts of Finite Type and Factors of Gibbs Measures"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0986-8044","authenticated-orcid":false,"given":"Uijin","family":"Jung","sequence":"first","affiliation":[{"name":"Department of Mathematics, Ajou University, 206 Worldcup-ro, Suwon 16499, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,11,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1007\/BF02761605","article-title":"Equivalence of topological Markov shifts","volume":"27","author":"Adler","year":"1977","journal-title":"Israel J. 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