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arXiv · 2401.01499

The Lyapunov spectrum as the Newton-Raphson method for countable Markov interval maps

Nicolás Arévalo H
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Abstract

We consider MRL maps (Markov-Renyi-L\"uroth), 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 $-t\log|T'|$.

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Nicolás Arévalo H. 2024-01-03. The Lyapunov spectrum as the Newton-Raphson method for countable Markov interval maps. https://arxiv.org/abs/2401.01499

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