For more information about this meeting, contact Anatole Katok.
| Title: | Equilibrium States and Equidistribution of Periodic Orbits in a Non-Uniform, Non-Markov Setting |
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| Seminar: | Center for Dynamics and Geometry Seminar |
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| Speaker: | Dan Thompson, Penn State |
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| Abstract: |
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| 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
| Room Number: | MB106 |
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| Date: | 10 / 03 / 2011 |
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| Time: | 03:35pm - 05:30pm |
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