Gonchenko S. V., Gordeeva O. V., Lukyanov V. I., Ovsyannikov I. I.
On Bifurcations of Multidimensional Diffeomorphisms Having a Homoclinic Tangency to a Saddle-node
2014, vol. 19, no. 4, pp. 461-473
We study the main bifurcations of multidimensional diffeomorphisms having a nontransversal 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 neighborhood of the homoclinic orbit. Also, a relation of our results to the 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.