Averaging Result for Differential Equations Perturbed by a Z-Periodic Lorentz Gas
Explore a 47-minute conference talk on averaging results for differential equations perturbed by a Z-periodic Lorentz gas, presented at the Workshop on "Rare Events in Dynamical Systems" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the study of differential equations with vector fields perturbed by the fast motion of particles in a cylinder, corresponding to the Z-periodic Lorentz gas model introduced by H.A Lorentz in 1905. Examine the asymptotic behavior of solutions when the dynamic accelerates, comparing known results for probability-preserving dynamical systems with the infinite measure-preserving Lorentz gas. Investigate the averaging result expressed as a limit theorem, providing the rate of convergence of the perturbed equation's solution to an averaged ordinary differential equation. Gain insights into the main features of the limit process and the proof methodology based on a limit theorem for non-stationary ergodic sums on the Z-periodic Lorentz gas. Read more