I will present a method to perturb expanding endomorphisms of the two-torus in order to obtain conservative endomorphisms with one positive and one negative Lyapunov exponent at Lebesgue almost every point. The examples are C^1 robust, stably ergodic, and the Lyapunov exponents and the metric entropy depend continuously on the map.

This is joint work with Martin Andersson and Pablo Carrasco.