  The asymptotic sectional hyperbolicity is a weak notion of hyperbolicity that
extends properly the sectional-hyperbolicity and includes the Rovella attractor
as a archetypal example. The main feature of this definition is the existence
of arbitrarily large hyperbolic times for points outside the stable manifolds
of the singularities. In this paper we will prove that any attractor associated
to a $C^1$ vector field $X$ on a three-dimensional manifold satisfying this
kind of hyperbolicity is rescaling-expansive and presents sensitiveness respect
to initial conditions.
