Felipe Pérez Pereira
Published 2018-12-11Version 1
We study the Hausdorff dimension of Gibbs measures with infinite entropy with respect to maps of the interval with countably many branches. We show that under simple conditions, such measures are symbolic-exact dimensional, and provide an almost sure value for the symbolic dimension. We also show that the lower local dimension dimension is almost surely equal to zero, while the upper local dimension is almost surely equal to the symbolic dimension. In particular, we prove that a large class of Gibbs measures with infinite entropy for the Gauss map have Hausdorff dimension zero and packing dimension equal to $1/2$, and so such measures are not exact dimensional.
On generators with infinite entropy
Central limit theorem for dimension of Gibbs measures for skew expanding maps
Parametrized Families of Gibbs Measures and their Statistical Inference
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