School on Hyperbolic Dynamics

# seminar: Phase Transitions of the Multifractal Spectrum for Countably Branched Expanding Markov Maps

speaker: Jason Tomas Dungca (University of Bristol)

abstract: We consider the multifractal spectrum for countably branched expanding Markov maps that satisfy the big images property and topological mixing. These maps are each modelled by a countable Markov shift $$Sigma.$$ We consider the set of $$x \in \Sigma$$ that have local dimension $$\alpha \ge 0$$ for some Gibbs measure. The multifractal spectrum is a function that gives the Hausdorff dimension of each of these sets that have local dimension $$\alpha.$$ For finite state Markov shifts, the multifractal spectrum for Gibbs measures is analytic everywhere on its domain. However, for countable state Markov shifts, the multifractal spectrum can have phase transitions and we will then apply our results to the Gauss map.

timetable:
Tue 13 Jun, 16:20 - 16:40, Aula Dini
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