A C 1-generic dichotomy for diffeomorphisms: Weak forms of hyperbolicity or infinitely many sinks or sources By C. Bonatti, L. J. D´ ıaz, and E. R. Pujals* A Ricardo Ma˜e (1948–1995), por todo su trabajo n´ Abstract We show that, for every compact n-dimensional manifold, n ≥ 1, there is a residual subset of Diff1 (M ) of diffeomorphisms for which the homoclinic class of any periodic saddle of f verifies one of the following two possibilities: Either it is contained in the closure of an infinite set of sinks or sources (Newhouse phenomenon), or it presents some weak form of.
