In this work, we study ergodic properties of some attractors "beyond uniform hyperbolicty", our interest is the existence and finiteness of physical measures. We are going to deal with 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 (non-integrability of Es+Eu), neutrality in the central direction and regularity of the stable foliation admits a nite 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.