Existence and smoothness of the stable foliation for sectional hyperbolic attractors

Bull. London Math. Soc. 49 (2017) 351-367.

Vitor Araújo and Ian Melbourne

Abstract

We prove the existence of a contracting invariant topological foliation in a full neighborhood for sectional hyperbolic attractors. Under certain bunching conditions it can then be shown that this stable foliation is smooth. In particular, we show that the stable foliation for the classical Lorenz equation (and nearby vector fields) is better than C¹ which is crucial for recent results on exponential decay of correlations. In fact the foliation is at least C^1.264.