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arXiv · 1604.06924

Existence and smoothness of the stable foliation for sectional hyperbolic attractors

V. Araújo·I. Melbourne
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Abstract

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

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V. Araújo, I. Melbourne. 2016-04-23. Existence and smoothness of the stable foliation for sectional hyperbolic attractors. https://doi.org/10.1112/blms.12037

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