Area-preserving diffeomorphisms of the torus whose rotation sets have non-empty interior

In this paper we consider C1+ ε area-preserving diffeomorphisms of the torus f , either homotopic to the identity or to Dehn twists. We suppose that f has a lift f to the plane such that its rotation set has interior and prove, among other things, that if zero is an interior point of the rotation set, then there exists a hyperbolic f -periodic point Q ∈ R ² such that Wᵘ ( Q ) intersects Wˢ ( Q + (a, b)) for all integers $(a, b)$ , which implies that Wᵘ ( Q ) is invariant under integer translations. Moreover, Wᵘ ( Q ) = Wˢ ( Q ) and f restricted to Wᵘ ( Q ) is invariant and topologically mixing. Each connected component of the complement of Wᵘ ( Q ) is a disk with diameter uniformly bounded from above. If f is transitive, then Wᵘ ( Q ) = R ² and f is topologically mixing in the whole plane.