Multifractal analysis for multimodal maps

Mike Todd

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arXiv · 0809.1074

Multifractal analysis for multimodal maps

Mike Todd

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Abstract

Given a multimodal interval map $f:I \to I$ and a Hölder potential $ϕ:I \to \mathbb{R}$, we study the dimension spectrum for equilibrium states of $ϕ$. The main tool here is inducing schemes, used to overcome the presence of critical points. The key issue is to show that enough points are `seen' by a class of inducing schemes. We also compute the Lyapunov spectrum. We obtain the strongest results when $f$ is a Collet-Eckmann map, but our analysis also holds for maps satisfying much weaker growth conditions.

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BibTeX RIS

Mike Todd. 2009-11-16. Multifractal analysis for multimodal maps. https://arxiv.org/abs/0809.1074

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