Existence and smoothness of the stable foliation for sectional hyperbolic attractors

摘要

We prove the existence of a contracting invariant topological foliation in afull neighborhood for partially hyperbolic attractors. Under certain bunchingconditions it can then be shown that this stable foliation is smooth.Specialising to sectional hyperbolic attractors, we give a verifiable conditionfor bunching. In particular, we show that the stable foliation for theclassical Lorenz equation (and nearby vector fields) is better than $C^1$ whichis crucial for recent results on exponential decay of correlations. In fact thefoliation is at least $C^{1.278}$.