  In this work, we study ergodic properties of certain partially hyperbolic
attractors whose central direction has a neutral behavior, the main feature is
a condition of transversality between unstable leaves when projected by the
stable holonomy. We prove that partial hyperbolic attractors satisfying
conditions of transversality between unstable leaves via the stable holonomy,
neutrality in the central direction and regularity of the stable foliation
admits a finite number of physical measures, coinciding with the ergodic
u-Gibbs States, whose union of the basins has full Lebesgue measure. Moreover,
we describe the construction of a family of robustly nonhyperbolic attractors
satisfying these properties.
