Partially hyperbolic and transitive dynamics generated by heteroclinic cycles

We study C-k-diffeomorphisms, k greater than or equal to 1, f : M --> M, ex hibiting hetero-dimensional cycles (i.e, cycles containing periodic points of different stable indices). We prove that if f can not be Ck-approximated by diffeomorphisms with homoclinic tangencies, then f is in the closure of an open set U subset of Diff(k) (M) consisting of diffeomorphisms g with a non-hyperbolic transitive set hg which is locally maximal and strongly par tially hyperbolic (the partially hyperbolic splitting at hg has three non-t rivial directions). As a consequence, in the case of 3-manifolds, we give n ew examples of open sets of C-1-diffeomorphisms for which residually infini tely many sinks or sources coexist (C-1-Newhouse's phenomenon). We also pro ve that the occurrence of non-hyperbolic dynamics has persistent character in the unfolding of heterodimensional cycles.