On bifurcations of multidimensional diffeomorphisms having a homoclinic tangency to a saddle-node
Dynamical Systems
2014-12-03 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1412.0932,
title = {On bifurcations of multidimensional diffeomorphisms having a homoclinic tangency to a saddle-node},
author = {S. V. Gonchenko and O. V. Gordeeva and V. I. Lukjanov and I. I. Ovsyannikov},
journal= {arXiv preprint arXiv:1412.0932},
year = {2014}
}