Hereditary subshifts whose measure of maximal entropy has no Gibbs\n property

2020/04/16 by Joanna Kułaga-Przymus, Kułaga-Przymus, Joanna, Michał Lemańczyk +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Cellular Automata and Applications #Combinatorics #Computer science #Converse #Data mining #Discrete mathematics #Dynamical Systems (math.DS) #Entropy (arrow of time) #FOS: Mathematics #Geometry #Gibbs measure #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Measure (data warehouse) #Philosophy #Physics #Probability (math.PR) #Property (philosophy) #Pure mathematics #Receptor Mechanisms and Signaling #Thermodynamics #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2004.07643

openalex publication_date 2020/04/16 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We show that the measure of maximal entropy for the hereditary closure of a\n mathscrB-free subshift has the Gibbs property if and only if the Mirsky\nmeasure of the subshift is purely atomic. This answers an open question asked\nby Peckner. Moreover, we show that mathscrB is taut whenever the\ncorresponding Mirsky measure \ν_\η has full support. This is the converse\ntheorem to a recent result of Keller.\n

Citations

• On sequences of positive integers
• GIBBS MEASURES IN ERGODIC THEORY
• Representations for real numbers and their ergodic properties
• Dynamics on the graph of the torus parametrization

Related

• Equilibrium states which are not Gibbs measure on hereditary subshifts
• Hereditary subshifts whose simplex of invariant measures is Poulsen
• Invariant measures for \mathscrB-free systems revisited
• Measures of maximal relative entropy
• Maximizing measures of generic Hölder functions have zero entropy