INFINITELY MANY COEXISTING STRANGE ATTRACTORS

We prove that C-infinity diffeomorphisms of a two-dimension manifold M with a homoclinic tangency are in the closure of an open set of Diff( infinity) (M) containing a dense subset of diffeomorphisms exhibiting infinitely many coexisting Henon-like strange attractors (or repellers ). A similar statement is posed in terms of one-parameter C-infinity f amilies of diffeomorphisms unfolding a homoclinic tangency. Moreover, we show the existence of infinitely many dynamical phenomena others th an strange attractors. (C) Elsevier, Paris.