Thermodynamical formalism for higher dimensional maps

Samuel Anton Senti (UFRJ)

Resumo: We show how inducing schemes for multidimensional maps can be used to describe the potential functions for which existence (and uniqueness) of equilibrium measures can be proven. This will be illustrated with a few examples with Gibbs-Markov-Young towers (including the Hénon maps and Katok's example). Whereas in general the class of invariant measures for which this thermodynamical formalism applies may not encompass all invariant measures, we will illustrate certain examples where this
is the case. Time permitting we will explain how extra information on the inducing scheme ensures that all measures can be accounted for through this formalism.

This is a joint work with Y. Pesin and K. Zhang