Entropy in uniformly quasiregular dynamics
| Autor: | Ilmari Kangasniemi, Yûsuke Okuyama, Tuomas Sahlsten, Pekka Pankka |
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| Přispěvatelé: | Department of Mathematics and Statistics, Geometric Analysis and Partial Differential Equations |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Conjecture Applied Mathematics General Mathematics 010102 general mathematics Metric Geometry (math.MG) Topological entropy Dynamical Systems (math.DS) uniformly quasiregular mappings 01 natural sciences Homology sphere Primary 30C65 Secondary 57M12 30D05 Entropy (classical thermodynamics) Mathematics - Metric Geometry 0103 physical sciences 111 Mathematics FOS: Mathematics 010307 mathematical physics Mathematics - Dynamical Systems 0101 mathematics entropy Ahlfors regular metric space Mathematics |
| DOI: | 10.48550/arxiv.1903.10183 |
| Popis: | Let $M$ be a closed, oriented, and connected Riemannian $n$-manifold, for $n\ge 2$, which is not a rational homology sphere. We show that, for a non-constant and non-injective uniformly quasiregular self-map $f\colon M\to M$, the topological entropy $h(f)$ is $\log \mathrm{deg}( f )$. This proves Shub's entropy conjecture in this case. Comment: 31 pages, v3: streamlined the proof of the entropy lower bound based on comments from P. Ha\"issinsky. Also stated some more general versions of the lower bound result, and fixed various typos throughout the paper |
| Databáze: | OpenAIRE |
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