On Escape rate for subshift with Markov measure
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914826280763392 |
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| author | Agarwal, Nikita Cheriyath, Haritha Tikekar, Sharvari Neetin |
| author_facet | Agarwal, Nikita Cheriyath, Haritha Tikekar, Sharvari Neetin |
| contents | In this paper, we consider a subshift of finite type with Markov measure. By considering a union of cylinders as holes, we investigate the exponential growth rate of measure of points whose orbits do not escape into the hole over a fixed number of iterations. We present two formulations for this escape rate: one based on the spectral radius of the Hadamard product of a related adjacency matrix and the stochastic matrix with respect to which the Markov measure is defined, and the other utilizing a recurrence relation. These formulations enable a comparative analysis of escape rates into distinct holes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05118 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Escape rate for subshift with Markov measure Agarwal, Nikita Cheriyath, Haritha Tikekar, Sharvari Neetin Dynamical Systems In this paper, we consider a subshift of finite type with Markov measure. By considering a union of cylinders as holes, we investigate the exponential growth rate of measure of points whose orbits do not escape into the hole over a fixed number of iterations. We present two formulations for this escape rate: one based on the spectral radius of the Hadamard product of a related adjacency matrix and the stochastic matrix with respect to which the Markov measure is defined, and the other utilizing a recurrence relation. These formulations enable a comparative analysis of escape rates into distinct holes. |
| title | On Escape rate for subshift with Markov measure |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2401.05118 |