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.