Seminar 10.10.13

Localized Pressure and Equilibrium States


Oct 10 2013 – 3:00pm – 4:00 pm




Tamara Kucherenko (CUNY)


We introduce the notion of localized topological pressureĀ 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 theĀ 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)