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Multifractal analysis of weak Gibbs measures for non-uniformly expanding C1 maps

Published online by Cambridge University Press:  18 January 2010

THOMAS JORDAN  and
MICHAŁ RAMS
THOMAS JORDAN
Affiliation:
Department of Mathematics, The University of Bristol, University Walk, Clifton, Bristol BS8 1TW, UK (email: thomas.jordan@bristol.ac.uk)
MICHAŁ RAMS
Affiliation:
Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-956 Warszawa, Poland (email: M.Rams@impan.gov.pl)
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Abstract

We will consider the local dimension spectrum of a weak Gibbs measure on a C1 non-uniformly hyperbolic system of Manneville–Pomeau type. We will present the spectrum in three ways: using invariant measures, ergodic invariant measures supported on hyperbolic sets and equilibrium states. We are also proving analyticity of the spectrum under additional assumptions. All three presentations are well known for smooth uniformly hyperbolic systems.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 1 , February 2011 , pp. 143 - 164
Copyright
Copyright © Cambridge University Press 2009

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