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This article is cited in 2 scientific papers (total in 2 papers)
On Bifurcations of Multidimensional Diffeomorphisms Having a Homoclinic Tangency to a Saddle-node
Sergey V. Gonchenkoa, Îlga V. Gordeevaa, Valery I. Lukyanova, Ivan I. Ovsyannikovab a Nizhny Novgorod State University,
pr. Gagarina, 23, Nizhny Novgorod, 603000 Russia
b Imperial College, SW7 2 AZ London, UK
Abstract:
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.
Received: 20.03.2014 Accepted: 24.04.2014
Citation:
Sergey V. Gonchenko, Îlga V. Gordeeva, Valery I. Lukyanov, Ivan I. Ovsyannikov, “On Bifurcations of Multidimensional Diffeomorphisms Having a Homoclinic Tangency to a Saddle-node”, Regul. Chaotic Dyn., 19:4 (2014), 461–473
Linking options:
https://www.mathnet.ru/eng/rcd173 https://www.mathnet.ru/eng/rcd/v19/i4/p461
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Abstract page: | 151 | References: | 34 |
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