## DYNAMICAL SYSTEMS Seminar

### The Rovella attractor is asymptotically sectional-hyperbolic

Bernardo San Martin
Abstract: The Rovella attractor is a compact invariant set for a vector field $X_0$ constructed in a similar way as the geometric Lorenz attractor, but replacing the central expansive condition at the singularity by a central contracting condition plus two additional geometric hypothesis: the unstable manifold of the singularity is contained in the stable manifold of hyperbolic periodic orbits and the one dimensional reduction for the first return Poincar\'e map has negative Schwarzian derivative. Rovella showed that although this attractor is non robust, it is almost 2-persistent in the $C^3$ topology. In this paper we will prove that for a generic two-parameter family of vector fields that contains $X_0$, asymptotically sectional-hyperbolicity is an almost 2-persistent property. In particular, we will prove that the Rovella attractor is asymptotically sectional-hyperbolic.