Powerpoint( 2000) version:

talk3.ppt

Diffusion approximation for billiards (plan)
1.  Presentation of billiards models
2.The dynamic system approach:
        2.1 Notations
        2.1 Definitions
        2.2 Fundamental results (1)
        2.2 Fundamental results (2)
        2.3 Diffusion approximation for finite horizon billiards
        2.4 Infinite horizon billiards. Anomalous diffusion (1)
        2.4 Infinite horizon billiards. Anomalous diffusion (2)
        2.5 Numerical simulations (1)
        2.5 Numerical simulations (2)
        2.5 Numerical simulations (3)
3.The PDE approach:
        3.1 The Liouville equation
        3.1 Boundary condition
        3.2 A compacity result
        3.2 Idea of the proof
        3.3 The diffusion approximation result
        3.3 The diffusion coefficient
        3.3 Sketch of the proof
4.  Conjectures. Future work