Averaging theorems for slow fast systems in ℤ-extensions (discrete time)

2024/01/20 by Maxence Phalempin, Phalempin, Maxence
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2401.11277

openalex publication_date 2024/01/20 · openalex created_date 2024/01/24 · openalex updated_date 2026/08/01

Abstract

We study the averaging method for flows perturbed by a dynamical system preserving an infinite measure. Motivated by the case of perturbation by the collision dynamic on the finite horizon \mathbb Z-periodic Lorentz gas and in view of future development, we establish our results in a general context of perturbation by \mathbb Z-extension over chaotic probability preserving dynamical systems. As a by product, we prove limit theorems for non-stationary Birkhoff sums for such infinite measure preserving dynamical systems.

Related

• Slow-fast systems in infinite measure, with or without averaging
• Limit theorems for Birkhoff sums and local times of the periodic Lorentz gas with infinite horizon
• Central limit theorems for the ℤ²-periodic Lorentz gas
• On almost-sure versions of classical limit theorems for dynamical systems
• On the study of slow-fast dynamics, when the fast process has multiple invariant measures