Multifractal analysis of weak Gibbs measures for non-uniformly expanding <i>C</i>¹ maps

Abstract

Abstract We will consider the local dimension spectrum of a weak Gibbs measure on a C 1 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.