Thermodynamics via Inducing

Dynamics Student Seminar

Meeting Details

For more information about this meeting, contact Kristin Berrigan, Alp Uzman.

Speaker: Farruh Shahidi, Penn State

Abstract: We consider continuous maps $f: X \to X$ on compact metric spaces admitting inducing schemes of hyperbolic type as well as the induced maps $\tilde{f} : \tilde{X}\to\tilde{X}$ and the associated tower maps $\hat{f}:\hat{X}\to\hat{X}.$ For a certain class of potential functions on $X$, which includes all Holder continuous functions, we establish thermodynamic formalism for each of the above three systems and we describe some relations between the corresponding equilibrium measures. Furthermore we study ergodic properties of these equilibrium measures including the Bernoulli property, decay of correlations, and the Central Limit Theorem (CLT). Finally, we prove analyticity of the pressure function for the three systems (joint with A. Zelerowicz).

Room Reservation Information

Room Number: 106 McAllister

Date: 01/17/2019

Time: 5:30pm - 8:00pm