Robust exponential decay of correlations for singular-flows

TL;DR

This paper demonstrates that certain singular-flow systems, including the geometric Lorenz attractor, exhibit robust exponential decay of correlations, indicating strong statistical mixing properties.

Contribution

It constructs open sets of smooth vector fields with singularities that have proven exponential decay of correlations, including the geometric Lorenz attractor.

Findings

Robust exponential decay of correlations for singular flows.

Application to the geometric Lorenz attractor.

Establishment of decay properties for open sets of vector fields.

Abstract

We construct open sets of Ck (k bigger or equal to 2) vector fields with singularities that have robust exponential decay of correlations with respect to the unique physical measure. In particular we prove that the geometric Lorenz attractor has exponential decay of correlations with respect to the unique physical measure.