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Regular and Chaotic Dynamics, 2014, Volume 19, Issue 4, Pages 461–473
DOI: https://doi.org/10.1134/S1560354714040029 (Mi rcd173) 		 
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
Citations (2)
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DOI: https://doi.org/10.1134/S1560354714040029
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.
Funding agency Grant number
Russian Science Foundation 14-12-00811
Russian Foundation for Basic Research 13-01-00589
3-01-97028-povolzhje
14-01-00344
Ministry of Education and Science of the Russian Federation 02.B.49.21.0003
Leverhulme Trust RPG-279
Engineering and Physical Sciences Research Council EP/I019111/1
Sections 5 and 6 are carried out by the RSF-grant (project No. 14-12-00811). The paper was partially supported by the grants of RFBR No. 13-01-00589, 3-01-97028–povolzhje and 14-01-00344. SG was supported by the grant (the agreement of August 27, 2013 No. 02.B.49.21.0003 between The Ministry of education and science of the Russian Federation and Lobachevsky State University of Nizhni Novgorod). IO was supported by the Leverhulme Trust grant RPG-279 and the EPSRC Mathematics Platform grant EP/I019111/1.
Received: 20.03.2014
Accepted: 24.04.2014
Bibliographic databases:
Document Type: Article
MSC: 37C05, 34C37, 37C29, 37G25
Language: English
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
Citation in format AMSBIB
\Bibitem{GonGorLuk14}
\by Sergey~V.~Gonchenko, Îlga~V.~Gordeeva, Valery~I.~Lukyanov, Ivan~I.~Ovsyannikov
\paper On Bifurcations of Multidimensional Diffeomorphisms Having a Homoclinic Tangency to a Saddle-node
\jour Regul. Chaotic Dyn.
\yr 2014
\vol 19
\issue 4
\pages 461--473
\mathnet{http://mi.mathnet.ru/rcd173}
\crossref{https://doi.org/10.1134/S1560354714040029}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3240979}
\zmath{https://zbmath.org/?q=an:1337.37018}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000340380900002}
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  • https://www.mathnet.ru/eng/rcd/v19/i4/p461
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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