## Localized Pressure and Equilibrium States

### Time

Oct 10 2013 – 3:00pm – 4:00 pm

### Location

MW154

### Speaker

Tamara Kucherenko (CUNY)

### Abstract

We introduce the notion of localized topological pressure for continuous maps on compact metric spaces and establish a local version of the variational principle for several classes of dynamical systems and potentials. We also construct examples showing that the assumptions in the localized variational principle are fairly sharp. Next, we study localized equilibrium states and show that even in the case of subshifts of finite type and Holder continuous potentials, there are several new phenomena that do not occur in the theory of classical equilibrium states. In particular, ergodic localized equilibrium states for Holder continuous potentials are in general not unique. (joint work with C.Wolf)