Chaos in expanding Baker-like maps

In this work, we consider a discontinuous piecewise monotone map f of the interval[0; 1] onto itself, with N 2 branches. That is, Lorenz maps for N = 2 and a familyof expanding Baker-like maps for N > 2. We determine the necessary and su cient conditions to have chaos in the whole interval. This condition, which we call of fullchaos, is very important in engineering applications, especially those related to grazing bifurcations, as well as in other applied elds.