Journal
ERGODIC THEORY AND DYNAMICAL SYSTEMS
Volume 23, Issue -, Pages 1751-1784Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/S0143385703000051
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For a given expanding d-fold covering transformation of the one-dimensional torus, the notion of weak Gibbs measure is defined by a natural generalization of the classical Gibbs property. For these measures, we prove that the singularity spectrum and the L-q -spectrum form a Legendre transform pair. The main difficulty comes from the possible existence of first-order phase transition points, that is, points where the Lit -spectrum is not differentiable. We give examples of weak Gibbs measure with phase transition, including the so-called Erdos measure.
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