In this talk we discuss some mechanisms of destruction of dynamics.  We start with a horseshoe and study the variation of the topological entropy after bifurcating an internal tangency through a one-parameter family. Using geometrical methods, we prove that, for a big set of parameters, the topological entropy is a non-increasing function. This result formalizes the idea that the loss of transversal homoclinic intersections implies the decreasing of the amount of dynamics.