Erratum to: Robust Exponential Decay of Correlations for Singular-Flows

Abstract

In this erratum, we show how to complete the proof of TheoremA. Consequently, the main result in the original article remains valid. The need for possible higher smoothness of the vector field to be in a certain conjugation class is a direct consequence of a classical result of Hartman [3, Theorem 12.1, p. 257] stated also in Theorem 3.2 of the original article. Let s ≥ 2 and let U be a CN -open set of vector fields that exhibit a Lorenz attractor and let r : → R+ denote the roof function obtained by conjugation to a suspension flow with a global cross-section . The good hyperbolic skew-product semiflow condition consists of exponential tail estimates for the roof function, smoothness of the disintegration of the SRB measure and a non-uniform integrability (UNI) condition; see Sect. 2 of the original article. The argument in Sect. 4.4 of the original article to prove smoothness of the disintegration of the SRBmeasure along stablemanifolds lacks some details that were recently completed by Butterley and Melbourne in [2]. Since the last estimate in the argument in Sect. 4.2.3 of the original article is not enough to guarantee the uniform non-integrability condition claimed, the goal of this erratum is to provide an alternative proof to the uniform non-integrability condition. The argument in Sect. 4.2.3 of the original article must