Dynamical Systems Seminar

A formula for the Hausdorff dimension of invariant ergodic probability measures holds for a large class of dynamical systems:

Hausdorff dimension = metric entropy/Lyapunov exponent

This formula connects geometric properties of the measure to dynamical quantities of the system. One of the essential assumptions of this formula, is that the entropy of the measure is finite. In this talk, I will show that for a certain class of maps modelled by a countable Markov shift and a class of Gibbs/Bernoulli measures with infinite entropy, it is possible to compute the local dimensions almost everywhere and consequently, obtain the values of the Hausdorff and the packing dimension of the measure.