Dynamical Systems and Ergodic Theory, PHD course 2025/2026
<br> 
Lectures:
<ol>
<li> Lecture of the 11/11/2025: Tension between micro anf macro.
<li> Lecture of the 13/11/2025: An example of instability: pendulum with oscillating suspension point.
<li> Lecture of the 18/11/2025: Measurable dynamical systems. Ergodicity, Birkhoff, Von Neumann.
<li> Lecture of the 20/11/2025: Recurrence (Poincar&egrave, Kac). Mixing. Bernoulli.
<li> Lecture of the 25/11/2025: Establishing Ergodicity: the Hopf argument in a symple case.
<li> Lecture of the 27/11/2025: Two spheres in a Torus and Sinai Billiards.
<li> Lecture of the 01/12/2025: Sinai version of Hopf argument. 
<li> Lecture of the 03/12/2025: Hyperbolicity, Lyapunov exponents and invariant manifolds. 
<li> Lecture of the 10/12/2025: How to establish hyperbolicity in Hamiltonian systems.
<li> Lecture of the 15/12/2025: Hypberbolic of billiards and of a gas of hard spheres.