Almost sure convergence of cover times for $\psi $ -mixing systems
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| Názov: | Almost sure convergence of cover times for $\psi $ -mixing systems |
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| Autori: | BOYUAN ZHAO |
| Prispievatelia: | University of St Andrews.Pure Mathematics |
| Zdroj: | Ergodic Theory and Dynamical Systems. :1-17 |
| Publication Status: | Preprint |
| Informácie o vydavateľovi: | Cambridge University Press (CUP), 2025. |
| Rok vydania: | 2025 |
| Predmety: | Irrational rotations, Minkowski dimension, T-NDAS, FOS: Mathematics, Exponentially ψ-mixing, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, Cover time, 37A25, 37E05, 37E10 |
| Popis: | Given a topologically transitive system on the unit interval, one can investigate the cover time, that is, the time for an orbit to reach a certain level of resolution in the repeller. We introduce a new notion of dimension, namely the stretched Minkowski dimension, and show that under mixing conditions, the asymptotics of typical cover times are determined by Minkowski dimensions when they are finite, or by stretched Minkowski dimensions otherwise. For application, we show that for countably full-branched affine maps, results using the usual Minkowski dimensions fail to give a finite limit of cover times, whilst the stretched version gives a finite limit. In addition, cover times for irrational rotations are calculated as counterexamples due to the absence of mixing. |
| Druh dokumentu: | Article |
| Popis súboru: | application/pdf |
| Jazyk: | English |
| ISSN: | 1469-4417 0143-3857 |
| DOI: | 10.1017/etds.2025.10216 |
| DOI: | 10.48550/arxiv.2412.17425 |
| Prístupová URL adresa: | http://arxiv.org/abs/2412.17425 https://hdl.handle.net/10023/32774 |
| Rights: | CC BY |
| Prístupové číslo: | edsair.doi.dedup.....7e9ab0f465bf1780b278db57e36da08a |
| Databáza: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | Given a topologically transitive system on the unit interval, one can investigate the cover time, that is, the time for an orbit to reach a certain level of resolution in the repeller. We introduce a new notion of dimension, namely the stretched Minkowski dimension, and show that under mixing conditions, the asymptotics of typical cover times are determined by Minkowski dimensions when they are finite, or by stretched Minkowski dimensions otherwise. For application, we show that for countably full-branched affine maps, results using the usual Minkowski dimensions fail to give a finite limit of cover times, whilst the stretched version gives a finite limit. In addition, cover times for irrational rotations are calculated as counterexamples due to the absence of mixing. |
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| ISSN: | 14694417 01433857 |
| DOI: | 10.1017/etds.2025.10216 |