Existence and smoothness of the stable foliation for sectional hyperbolic attractors
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 which is crucial for recent results on exponential decay of correlations. In fact the foliation is at least .
Keywords
Cite
@article{arxiv.1604.06924,
title = {Existence and smoothness of the stable foliation for sectional hyperbolic attractors},
author = {V. Araújo and I. Melbourne},
journal= {arXiv preprint arXiv:1604.06924},
year = {2017}
}
Comments
Corrected estimate for smoothness of stable foliation. Clarification of which results hold for general partially hyperbolic attractors. Some minor typos fixed. Accepted for publication in Bull. London Math. Soc