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We consider classes of partially hyperbolic diffeomorphism $f:M\to M$ withsplitting $TM=E^s\oplus E^c\oplus E^u$ and $\dim E^c=2$. These classes includefor instance (perturbations of) the product of Anosov and conservative surfacediffeomorphisms, skew products of surface diffeomorphisms over Anosov,partially hyperbolic symplectomorphisms on manifolds of dimension four withbidimensional center foliation whose center leaves are all compact. We provethat accessibility holds in these classes for $C^1$ open and $C^r$ densesubsets and moreover they are stably ergodic.

Stable Ergodicity and Accessibility for certain Partially Hyperbolic Diffeomorphisms with Bidimensional Center Leaves