Abstract
AbstractI use a thermodynamic formalism to study the spectrumf(α) which characterises the large fluctuations of pointwise dimension in a Gibbs state supported on a hyperbolic cookie-cutter. Amongst other things, it is proved thatf(α) is the Hausdorff dimension of the set of points with pointwise dimension α, thatf(α) is real-analytic and that its Legendre transform τ(q) is related to the Renyi dimensionDqof the Gibbs state by the formula (1 −q)Dq= τ(q).
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