Intermittent quasistatic dynamical systems: weak convergence of fluctuations

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 influences. 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.

Keywords

• quasistatic dynamical system
• intermittency
• pomeau-manneville map
• weak convergence
• martingale problem
• 37c60
• 37d25
• 37a10
• 60g44
• 60h10