A class of differentiable toral maps which are topologically mixing

We show that on the 2-torus T-2 there exists a C-1 open set U of C-1 regula r maps such that every map belonging to U is topologically mixing but is no t Anosov. It was shown by Mane that this property fails for the class of C- 1 toral diffeomorphisms, but that the property does hold for the class of C -1 diffeomorphisms on the S-torus T-3. Recently Bonatti and Diaz proved tha t the second result of Mane is also true for the class of C-1 diffeomorphis ms on the n-torus T-n (n greater than or equal to 4).