On bifurcations of multidimensional diffeomorphisms having a homoclinic   tangency to a saddle-node
  We study main bifurcations of multidimensional diffeomorphisms having a non-transversal homoclinic orbit to a saddle-node fixed point. On a parameter plane we build a bifurcation diagram for single-round periodic orbits lying entirely in a small neighbourhood of the homoclinic orbit. Also a relation of our results to well-known codimension one bifurcations of a saddle fixed point with a quadratic homoclinic tangency and a saddle-node fixed point with a transversal homoclinic orbit is discussed. 
S.V. Gonchenko, O.V. Gordeeva, V.I. Lukjanov, I.I. Ovsyannikov
math.DS