Statistical stability for multidimensional piecewise expanding maps

TL;DR

This paper establishes conditions under which certain multidimensional piecewise expanding maps maintain their statistical properties under perturbations, demonstrating stability for a specific two-dimensional extension of tent maps.

Contribution

It provides new sufficient conditions for statistical stability in multidimensional settings and applies these to a novel two-dimensional tent map extension.

Findings

Sufficient conditions for strong statistical stability identified.

Two-dimensional tent map extension shown to be statistically stable.

Results extend classical one-dimensional stability concepts.

Abstract

We present sufficient conditions for the (strong) statistical stability of some classes of multidimensional piecewise expanding maps. As a consequence we get that a certain natural two-dimensional extension of the classical one-dimensional family of tent maps is statistically stable.