Intermittency in two dimensions

TL;DR

This paper introduces a new family of area-preserving maps extending the Pomeau-Manneville model to two dimensions, analyzing recurrence, correlations, transport, and effects of stochastic perturbations.

Contribution

It presents a novel two-dimensional extension of the Pomeau-Manneville family with analytical and numerical analysis of its dynamical properties.

Findings

Recurrence time distributions exhibit specific long-time behavior

Transport moments spectrum derived analytically

Stochastic perturbations influence dynamical properties

Abstract

We introduce a family of area-preserving maps representing a (non-trivial) two-dimensional extension of the Pomeau-Manneville family in one dimension. We analyze the long-time behavior of recurrence time distributions and correlations, providing analytical and numerical estimates. We study the transport properties of a suitable lift and use a probabilistic argument to derive the full spectrum of transport moments. Finally the dynamical effects of a stochastic perturbation are considered.