Building Thermodynamics for Non-Uniformly Hyperbolic Maps - Yakov Pesin

Explore the advanced mathematical concepts of building thermodynamics for non-uniformly hyperbolic maps in this comprehensive lecture. Delve into topics such as uniformly hyperbolic maps, the geometric potential, and symbolic models including countable Markov shifts. Examine the construction of equilibrium measures for the geometric t-potential using non-symbolic approaches. Investigate ergodic properties of SRB measures and equilibrium measures, and learn about the construction of SRB measures for chaotic attractors. Gain insights into the work of mathematicians like Sinai, Ruelle, Bowen, Aaronson-Denker, Mauldin-Urbanski, Sarig, Climenhaga, and Thompson as you navigate through this complex mathematical landscape.

Syllabus

Intro
The General Setting
Uniformly Hyperbolic Maps (Sinai, Ruelle, Bowen)
The Geometric Potential
Non-uniformly Hyperbolic Maps
Symbolic models I: Countable Markov Shifts. Aaronson-Denker, Mauldin-Urbanski, Sarig. Yuri
Symbolic models Ill: Nonuniform Specification, Climenhaga, Thompson
Constructing Equilibrium Measures For the Geometric t-potential: Non-symbolic Approach
Ergodic Properties: SRB Measures
Ergodic Properties: Equilibrium Measures
Constructing SRB Measures: Chaotic Attractors