Multifractal Analysis for Multimodal Maps
نویسنده
چکیده
Given a multimodal interval map f : I → I and a Hölder potential ' : I → R, we study the dimension spectrum for equilibrium states of '. 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 along critical orbits.
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