For more information about this meeting, contact Anatole Katok.
|Title:||Equilibrium States and Equidistribution of Periodic Orbits in a Non-Uniform, Non-Markov Setting|
|Seminar:||Center for Dynamics and Geometry Seminar|
|Speaker:||Dan Thompson, Penn State|
|This talk is an overview of recent joint work with Vaughn Climenhaga (Toronto). We establish uniqueness of equilibrium states for:
1) a large class of shift spaces which includes every beta-shift;
2) a large class of potential functions which strictly includes those with the Bowen property.
Under a mild additional hypothesis, we establish (weighted) equidistribution results for the periodic orbits of the space. I will introduce our techniques and discuss concrete applications of our general results. Some new results include: 1) Every subshift factor of a beta-shift has a unique measure of maximal entropy, answering an open problem of Mike Boyle; 2) For the beta-transformation, every Holder continuous potential has a unique equilibrium state; 3) These equilibrium states are characterized as weak limits of (weighted) periodic orbit measures. I plan to follow up this talk with one or two lectures in the Working Seminar, where I will give a more detailed exposition of our techniques and explain current work in progress, where we apply our techniques to some higher dimensional examples of geometric interest.|
Room Reservation Information
|Date:||10 / 03 / 2011|
|Time:||03:35pm - 05:30pm|