Cover times in dynamical systems
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866911887525937152 |
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| author | Jurga, Natalia Todd, Mike |
| author_facet | Jurga, Natalia Todd, Mike |
| contents | Given a one-dimensional dynamical system we study its cover time, which quantifies the rate at which orbits become dense in the state space. Using transfer operator tools for dynamical systems with holes and inducing techniques, for a wide class of uniformly hyperbolic and non-uniformly hyperbolic systems we obtain an asymptotic formula for the expected cover time in terms of the decay rate of the measure of the ball of minimum measure. Applications include the Gauss map and Manneville-Pomeau maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_05008 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Cover times in dynamical systems Jurga, Natalia Todd, Mike Dynamical Systems 37A25, 37E05, 37C30, 37D25, 37D35 Given a one-dimensional dynamical system we study its cover time, which quantifies the rate at which orbits become dense in the state space. Using transfer operator tools for dynamical systems with holes and inducing techniques, for a wide class of uniformly hyperbolic and non-uniformly hyperbolic systems we obtain an asymptotic formula for the expected cover time in terms of the decay rate of the measure of the ball of minimum measure. Applications include the Gauss map and Manneville-Pomeau maps. |
| title | Cover times in dynamical systems |
| topic | Dynamical Systems 37A25, 37E05, 37C30, 37D25, 37D35 |
| url | https://arxiv.org/abs/2204.05008 |