The Lyapunov spectrum as the Newton-Raphson method for countable Markov interval maps
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913184448774144 |
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| author | H, Nicolás Arévalo |
| author_facet | H, Nicolás Arévalo |
| contents | We consider MRL maps (Markov-Renyi-Lüroth), a class of interval maps with infinitely many branches that can have parabolic fixed points. We prove that for every MRL map $T$, the Lyapunov spectrum can be expressed in terms of the Legendre transform of the topological pressure of $-t\log|T'|$, generalizing previous results in the area. We also show that the Lyapunov spectrum coincides with a function directly related to the Newton-Raphson method applied to the topological pressure of $-t\log|T'|$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01499 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Lyapunov spectrum as the Newton-Raphson method for countable Markov interval maps H, Nicolás Arévalo Dynamical Systems Primary: 37A10, Secondary:37D35, 37H99 We consider MRL maps (Markov-Renyi-Lüroth), a class of interval maps with infinitely many branches that can have parabolic fixed points. We prove that for every MRL map $T$, the Lyapunov spectrum can be expressed in terms of the Legendre transform of the topological pressure of $-t\log|T'|$, generalizing previous results in the area. We also show that the Lyapunov spectrum coincides with a function directly related to the Newton-Raphson method applied to the topological pressure of $-t\log|T'|$. |
| title | The Lyapunov spectrum as the Newton-Raphson method for countable Markov interval maps |
| topic | Dynamical Systems Primary: 37A10, Secondary:37D35, 37H99 |
| url | https://arxiv.org/abs/2401.01499 |