Decomposition of infinite-to-one factor codes and uniqueness of relative\n equilibrium states

2017/05/01 by Ji‐Sang Yoo, Yoo, Jisang · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · #37A35 (Secondary) #37B10 (Primary) 37D35 #Algorithms and Data Compression #Cellular Automata and Applications #DNA and Biological Computing #Dynamical Systems (math.DS) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1705.00448

openalex publication_date 2017/05/01 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We show that an arbitrary factor map \π:X \→ Y on an irreducible subshift\nof finite type is a composition of a finite-to-one factor code and a class\ndegree one factor code. Using this structure theorem on infinite-to-one factor\ncodes, we then prove that any equilibrium state \ν on Y for a potential\nfunction of sufficient regularity lifts to a unique measure of maximal relative\nentropy on X. This answers a question raised by Boyle and Petersen (for lifts\nof Markov measures) and generalizes the earlier known special case of\nfinite-to-one factor codes.\n

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