Upper semi-continuity of entropy in non-compact settings
| Autor: | Mike Todd, Godofredo Iommi, Anibal Velozo |
|---|---|
| Přispěvatelé: | University of St Andrews. Pure Mathematics, University of St Andrews. School of Mathematics and Statistics |
| Rok vydání: | 2020 |
| Předmět: |
General Mathematics
T-NDAS 010102 general mathematics Dynamical Systems (math.DS) Computer Science::Digital Libraries 01 natural sciences Entropy (classical thermodynamics) Semi-continuity 37A05 37A35 FOS: Mathematics QA Mathematics Statistical physics Mathematics - Dynamical Systems 0101 mathematics QA Mathematics |
| Zdroj: | Mathematical Research Letters. 27:1055-1077 |
| ISSN: | 1945-001X 1073-2780 |
| DOI: | 10.4310/mrl.2020.v27.n4.a4 |
| Popis: | We prove that the entropy map for countable Markov shifts of finite entropy is upper semi-continuous at ergodic measures. Note that the phase space is non-compact. Applications to systems that can be coded by these shifts, such as positive entropy diffeomorphisms on compact manifolds, are given. We also discuss the related problem of existence of measures of maximal entropy. Comment: Some errors in applications corrected |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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