Singular hyperbolic attractors are statistical stable

TL;DR

This paper proves that the statistical properties of singular hyperbolic attractors, specifically the SRB measure, vary continuously with the dynamics, ensuring stability of their statistical behavior under perturbations.

Contribution

It establishes the continuous dependence of the SRB measure on the dynamics for singular hyperbolic attractors, a significant step in understanding their statistical stability.

Findings

SRB measure depends continuously on the dynamics

Statistical stability of singular hyperbolic attractors

Weak* topology convergence of measures

Abstract

We prove that the unique SRB measure for a singular hyperbolic attractor depends continuously on the dynamics in the weak$^\ast$ topology.