Multidimensional Rovella-like attractors
Abstract
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.
Keywords
Cite
@article{arxiv.0909.1033,
title = {Multidimensional Rovella-like attractors},
author = {V. Araujo and A. Castro and M. J. Pacifico and V. Pinheiro},
journal= {arXiv preprint arXiv:0909.1033},
year = {2012}
}
Comments
45 pages, 14 figures; improved introduction with more citations to other relevant related works. To appear in Journal of Differential Equations