Measure Complexity and Rigid Systems
| Autor: | Wen Huang, Run Ju Wei, Tao Yu, Xiao Min Zhou |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Applied Mathematics
General Mathematics 010102 general mathematics Topological entropy Characterization (mathematics) 01 natural sciences Measure (mathematics) 010101 applied mathematics Combinatorics Bounded function Metric (mathematics) Ergodic theory Invariant measure 0101 mathematics Dynamical system (definition) Mathematics |
| Zdroj: | Acta Mathematica Sinica, English Series. 38:68-84 |
| ISSN: | 1439-7617 1439-8516 |
| Popis: | In this paper we introduce two metrics: the max metric dn,q and the mean metric $${\bar d_{n,q}}$$ . We give an equivalent characterization of rigid measure preserving systems by the two metrics. It turns out that an invariant measure μ on a topological dynamical system (X, T) has bounded complexity with respect to dn,q if and only if μ has bounded complexity with respect to $${\bar d_{n,q}}$$ if and only if (X, $${\cal B}x$$ , μ, T) is rigid. We also obtain computation formulas of the measure-theoretic entropy of an ergodic measure preserving system (resp. the topological entropy of a topological dynamical system) by the two metrics dn,q and $${\bar d_{n,q}}$$ . |
| Databáze: | OpenAIRE |
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