Polynomial decay of correlations in linked-twist maps

TL;DR

This paper demonstrates that certain linked-twist maps, which are non-uniformly hyperbolic and generalize the Arnold Cat Map, exhibit polynomial decay of correlations at a rate of 1/n for Hölder observables.

Contribution

It establishes the polynomial decay rate of correlations for a class of linked-twist maps, extending understanding of their statistical properties.

Findings

Linked-twist maps have polynomial decay of correlations of order 1/n.

Decay of correlations applies to r-Hf6lder observables.

The results generalize known properties of hyperbolic maps to linked-twist maps.

Abstract

Linked-twist maps are area-preserving, piece-wise diffeomorphisms, defined on a subset of the torus. They are non-uniformly hyperbolic generalisations of the well-known Arnold Cat Map. We show that a class of canonical examples have polynomial decay of correlations for \alpha-H\"{o}lder observables, of order 1/n.