Dynamical Resistance Day

Title: Transfer operators, atomic decomposition and Besov spaces (video)

We use the method of atomic decomposition to study the action of transfer operators associated to piecewise expanding maps. It turns out that these transfer operators are quasi-compact even when the associated potential, the dynamics and the underlying phase space have very low regularity. In particular it is often possible to obtain exponential decay of correlations, the Central Limit Theorem and almost sure invariance principle for fairly general observables, including unbounded ones. Indeed the class of observables for which we obtain such results often coincides with certain Besov spaces. Joint work with Alexander Arbieto (UFRJ-Brazil)