The unique measure of maximal entropy for a compact rank one locally CAT(0) space
| Autor: | Russell Ricks |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Geodesic
Covering space Applied Mathematics 010102 general mathematics Metric Geometry (math.MG) Dynamical Systems (math.DS) Topological entropy 01 natural sciences Combinatorics Mathematics - Metric Geometry Maximal entropy Poincaré series 0103 physical sciences FOS: Mathematics Geodesic flow Mathematics::Metric Geometry Discrete Mathematics and Combinatorics Entropy (information theory) Mathematics::Differential Geometry 010307 mathematical physics Mathematics - Dynamical Systems 0101 mathematics Critical exponent Analysis Mathematics |
| Zdroj: | Discrete & Continuous Dynamical Systems - A. 41:507-523 |
| ISSN: | 1553-5231 |
| DOI: | 10.3934/dcds.2020266 |
| Popis: | Let $X$ be a compact, geodesically complete, locally CAT(0) space such that the universal cover admits a rank one axis. We prove the Bowen-Margulis measure on the space of geodesics is the unique measure of maximal entropy for the geodesic flow, which has topological entropy equal to the critical exponent of the Poincar\'e series. Comment: 15 pages |
| Databáze: | OpenAIRE |
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