Persistence of homoclinic tangencies in higher dimensions

In this paper we extend to a very general context Newhouse's phenomenon concerning the persistence of homoclinic tangencies and the coexistence of infinitely many sinks. This is done using the corresponding results in codimension one recently provedby J. Palis and M. Viana, and in a reduction of codimension in the unfolding of homoclinic tangencies developed in the present paper.