Averaging result for differential equations perturbed by a Z-periodic Lorentz gas.

by Dr Maxence Phalempin (Università degli studi di Firenze)

Tuesday 14 Nov 2023, 17:00 → 18:00 Europe/Rome

CRM - SNS

In this talk I present some differential equation perturbed by the fast motion of a particle in a cylinder corresponding to the Z-periodic Lorentz gas, a model introduced by H.A Lorentz in 1905. I will discuss there are one of the natural ways to extend the perturbed differential equations studied by Y.Kifer and Khasminskii for probability preserving Billiard transformations, to the infinite measure preserving Lorentz gas. I will state a limit theorem providing the rate of convergence of the solution of the perturbed equation to a solution of an averaged ordinary differential equation. After explaining the main features of the limit process,  I will give some idea of the proof based on the statement of a limit theorem for a non-stationary ergodic sum on a Z-periodic Lorentz gas