%0 Journal Article
%T Multidimensional Rovella-like attractors
%A V. Araujo
%A A. Castro
%A M. J. Pacifico
%A V. Pinheiro
%J Mathematics
%D 2009
%I arXiv
%R 10.1016/j.jde.2011.07.021
%X We present a multidimensional flow exhibiting a Rovella-like attractor: a transitive invariant set with a non-Lorenz-like singularity accumulated by regular orbits and a multidimensional non-uniformly expanding invariant direction. Moreover, this attractor has a physical measure with full support but persists along certain0909.1033 submanifolds of the space of vector fields. As in the 3-dimensional Rovella-like attractor, this example is not robust. The construction introduces a class of multidimensional dynamics, whose suspension provides the Rovella-like attractor, which are partially hyperbolic, and whose quotient over stable leaves is a multidimensional endomorphism to which Benedicks-Carleson type arguments are applied to prove non-uniform expansion.
%U http://arxiv.org/abs/0909.1033v4