Intermittent quasistatic dynamical systems: weak convergence of fluctuations

TL;DR

This paper studies the statistical behavior of non-stationary intermittent dynamical systems with slowly changing parameters, demonstrating their fluctuations converge weakly to a stochastic diffusion process.

Contribution

It extends previous results on quasistatic systems by analyzing intermittent maps, providing a diffusion approximation for their fluctuations under certain parameter conditions.

Findings

Fluctuations of intermittent quasistatic systems converge to a stochastic diffusion.

Results generalize prior work on expanding systems to intermittent maps.

Provides a martingale problem formulation for the diffusion limit.

Abstract

This paper is about statistical properties of quasistatic dynamical systems. These are a class of non-stationary systems that model situations where the dynamics change very slowly over time due to external influence. We focus on the case where the time-evolution is described by intermittent interval maps (Pomeau-Manneville maps) with time-dependent parameters. In a suitable range of parameters, we obtain a description of the statistical properties as a stochastic diffusion, by solving a well-posed martingale problem. The results extend those of a related recent study due to Dobbs and Stenlund, which concerned the case of quasistatic (uniformly) expanding systems.