On homoclinic tangencies, hyperbolicity, creation of homoclinic orbits and variation of entropy

We show that an assertion made in Gambaudo et al (1999 Nonlinearity 12 443) is not correct and, as a consequence, we confirm and even generalize previous results by those authors (Gambaudo and Rocha 1994 Nonlinearity 7 1251-9). Another main result states that variation of the topological entropy of surface diffeomorphisms is always associated with the unfolding of homoclinic tangencies.