Olga Gordeeva

pr. Gagarina, 23, Nizhny Novgorod, 603000 Russia
Nizhny Novgorod State University


Gonchenko S. V., Gordeeva O. V., Lukyanov V. I., Ovsyannikov I. I.
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.
Keywords: saddle-node, homoclinic tangency, Arnold tongues
Citation: 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, Regular and Chaotic Dynamics, 2014, vol. 19, no. 4, pp. 461-473

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