Thermodynamic Formalism CIRM Jean-Morlet Chair, Fall 2019

- Part I Specifications and Expansiveness. - 1. Beyond Bowen’s Specification Property. - 2. The Role of Continuity and Expansiveness on Leo and Periodic Specification Properties. - Part II Low Dimensional Dynamics and Thermodynamics Formalism. - 3. Thermodynamic Formalism and Geometric Applications for Transcendental Meromorphic and Entire Functions. - Part III Probability Theory Ergodicity and Thermodynamic Formalism. - 4. Recurrent Sets for Ergodic Sums of an Integer Valued Function. - 5. Almost Sure Invariance Principle for Random Distance Expanding Maps with a Nonuniform Decay of Correlations. - 6. Limit Theorem for Reflected Random Walks. - 7. The Strong Borel–Cantelli Property in Conventional and Nonconventional Setups. - 8. Application of the Convergence of the Spatio-Temporal Processes for Visits to Small Sets. - Part IV Geometry and Thermodynamics Formation. - 9. Rate of Mixing for Equilibrium States in Negative Curvature and Trees. - 10. Statistical Properties of the Rauzy-Veech-Zorich Map. - 11. Entropy Rigidity, Pressure Metric, and Immersed Surfaces in Hyperbolic 3-Manifolds. - 12. Higher Teichmüller Theory for Surface Groups and Shifts of Finite Type. - Part V Fractal Geometry. - 13. Dimension Estimates for C1 Iterated Function Systems and C1 Repellers, a Survey. - 14. Intermediate Dimensions: A Survey. - 15. Fractal Geometry of Bedford-McMullen Carpets. - 16. Some Variants of Orponen’s Theorem on Visible Parts of Fractal Sets.