Quasistatic dynamics with intermittency

TL;DR

This paper investigates the statistical behavior of a quasistatic dynamical system with intermittency, proving ergodic theorems and identifying physical measures for nonuniformly hyperbolic maps with changing parameters.

Contribution

It establishes ergodic theorems and characterizes physical measures for a class of intermittently chaotic systems with time-dependent parameters.

Findings

Almost sure convergence of time averages in certain parameter ranges

Identification of a unique physical family of measures

Convergence in probability in a broader parameter range

Abstract

We study an intermittent quasistatic dynamical system composed of nonuniformly hyperbolic Pomeau--Manneville maps with time-dependent parameters. We prove an ergodic theorem which shows almost sure convergence of time averages in a certain parameter range, and identify the unique physical family of measures. The theorem also shows convergence in probability in a larger parameter range. In the process, we establish other results that will be useful for further analysis of the statistical properties of the model.