Statistical Properties of Dynamical Systems, Spring 2025-2026.
Lectures:
  1. Lecture of 02/02/2026: Introduction.
  2. Lecture of 02/04/2026: Speed of convergence for ergodic averages for simple systems.
  3. Lecture of 02/09/2026: Smooth expanding maps and transfer operators.
  4. Lecture of 02/11/2026: Smooth expanding maps and invarinat measrues.
  5. Lecture of 02/16/2026: Smooth expanding maps and Lasota--Yorke inequality.
  6. Lecture of 02/18/2026: Hennion-Neussbaum theory.
  7. Lecture of 02/23/2026: Hennion-Neussbaum theory.
  8. Lecture of 02/25/2026: Hennion-Neussbaum theory.
  9. Lecture of 03/02/2026: Smooth expanding maps: spectrum of the transfer operator on different spaces.
  10. Lecture of 03/04/2026: Piecewise smooth expanding maps.
  11. Lecture of 03/09/2026: Expanding maps: Central Limit Theorem.
  12. Lecture of 03/11/2026: Expanding maps: Central Limit Theorem.
  13. Lecture of 03/23/2026: Expanding maps: Central Limit Theorem.
  14. Lecture of 03/25/2026: Expanding maps: Large deviations.
  15. Lecture of 03/30/2026: Standard pairs.
  16. Lecture of 04/01/2026: Standard pairs.
  17. Lecture of 04/06/2026: Non uniformly expanding maps.
  18. Lecture of 04/08/2026: Fixed point theorem and Hilbert metric.
  19. Lecture of 04/13/2026: Hilbert metric and spectral gap. Hyperbolic maps.
  20. Lecture of 04/15/2026: Hopf Argument. Invariant foliations.
  21. Lecture of 04/20/2026: Invariant foliations. Norms for hyperbolic maps.
  22. Lecture of 04/22/2026: Hyperbolic flows.