| Autor: |
Zhao, Boyuan |
| Předmět: |
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| Zdroj: |
Discrete & Continuous Dynamical Systems: Series A; Aug2024, Vol. 44 Issue 8, p1-28, 28p |
| Abstrakt: |
The shortest distance between the first $ n $ iterates of a typical point can be quantified with a log rule for some dynamical systems admitting Gibbs measures. We show this in two settings. For topologically mixing Markov shifts with at most countably infinite alphabet admitting a Gibbs measure with respect to a locally Hölder potential, we prove the asymptotic length of the longest common substring for a typical point converges and the limit depends on the Rényi entropy. For interval maps with a Gibbs-Markov structure, we prove a similar rule relating the correlation dimension of Gibbs measures with the shortest distance between two iterates in the orbit generated by a typical point. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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