Wild Lorenz like attractors

Abstract

We give the first examples of flows which exhibit robust singular attractors containing a wild hyperbolic set (in the sense of Newhouse). A hyperbolic set is said to be wild, if it has tangencies between its stable and unstable manifolds, in a robust way. The only restriction on the ambient manifold is that its dimension should be at least 5.

A revised and shorter version where only C^2 robust transitivity is shown. 39 pages, 2 figures