Multifractal analysis of weak Gibbs measures and phase transition—application to some Bernoulli convolutions

By De-Jun Feng, Eric Olivier. Ergodic Theory and Dynamical Systems, 2003

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Lyapunov Spectrum of Asymptotically Sub-additive Potentials (2009, background): “where μ is a weak Gibbs measure on a full shift space over finite symbols and In(x) denotes the n th cylinder about x (cf. [ 28 ] and Prop.”
Multifractal formalism for self-similar measures with weak separation condition (2009, methodology): “It is known that the measure satisfies the multifractal formalism [15].”
Lyapunov exponents for products of matrices and multifractal analysis. Part II: General matrices (2003, background): “Nevertheless, the multifractal formalism (for all 2 int(L )) of such a measure is proved to be valid by Feng and Olivier [ 17 ], which extended the partial results in [30, 43].”
The limited Rademacher functions and Bernoulli convolutions associated with Pisot numbers (2005, background): “by Feng and Olivier [ 18 ] by viewing as a weak Gibbs measure associated to some”