Abstract: We study billiard type systems whose reflections are not elastic. The existence of dominated splitting is proved for different cases. This means that tangent space splits into two invariant directions; the contractive behavior on one of them dominates the other one. We will explain the dynamical consequences of this property. The existence of attractors of different types is proved. We will present some numerical simulations and new exact results based in the method introduced in "Billiards with dominated Splitting" (ETDS, Markarian Pujals, Sambarino). Joint works with Aubin Arroyo and David Sanders (UNAM, México) and Sônia Pinto and Sylvie Oliffson (UFMG, Brazil).