Slow-fast systems in infinite measure, with or without averaging

2024/08/06 by Phalempin, Maxence
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2408.03009

Abstract

This paper studies the asymptotic behaviour of the solution of a differential equation perturbed by a fast flow preserving an infinite measure. This question is related with limit theorems for non-stationary Birkhoff integrals. We distinguish two settings with different behaviour: the integrable setting (no averaging phenomenon) and the case of an additive "centered" perturbation term (averaging phenomenon). The paper is motivated by the case where the perturbation comes from the Z-periodic Lorentz gas flow or from the geodesic flow over a Z-cover of a negatively curved compact surface. We establish limit theorems in more general contexts.

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