Multifractal analysis for multimodal maps

Details Multifractal analysis for multimodal maps Multifractal analysis for multimodal maps

2008-09-05

arxiv.org/abs/0809.1074v3

Mathematics

Dynamical Systems

Minor rewrites

Scientific paper

Given a multimodal interval map $f:I \to I$ and a H\"older potential $\phi:I \to \mathbb{R}$, we study the dimension spectrum for equilibrium states of $\phi$. 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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