Multidimensional Rovella-like attractors

Details Multidimensional Rovella-like attractors Multidimensional Rovella-like attractors

2009-09-05

arxiv.org/abs/0909.1033v4

J. Differential Equations 251 (2011) 3163-3201

Mathematics

Dynamical Systems

45 pages, 14 figures; improved introduction with more citations to other relevant related works. To appear in Journal of Diffe

Scientific paper

10.1016/j.jde.2011.07.021

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.

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