On-off intermittency and chaotic walks

TL;DR

This paper studies on-off intermittency in skew product maps over the doubling map, showing how chaotic walks driven by the doubling map exhibit intermittent behavior through Markov approximations.

Contribution

It introduces a novel analysis of on-off intermittency in skew product systems using Markov approximations of chaotic walks driven by the doubling map.

Findings

On-off intermittency occurs in the studied skew product maps.

Chaotic walks can be approximated by Markov random walks.

The analysis links intermittency to Lyapunov exponents at endpoints.

Abstract

We consider a class of skew product maps of interval diffeomorphisms over the doubling map. The interval maps fix the end points of the interval. It is assumed that the system has zero fiber Lyapunov exponent at one endpoint and zero or positive fiber Lyapunov exponent at the other endpoint. We prove the appearance of on-off intermittency. This is done using the equivalent description of chaotic walks: random walks driven by the doubling map. The analysis further relies on approximating the chaotic walks by Markov random walks, that are constructed using Markov partitions for the doubling map.