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Regular and Chaotic Dynamics, 2014, Volume 19, Issue 6, Pages 702–717
DOI: https://doi.org/10.1134/S1560354714060082 (Mi rcd193) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On Bifurcations of Area-preserving and Nonorientable Maps with Quadratic Homoclinic Tangencies

Amadeu Delshamsa, Marina Gonchenkob, Sergey V. Gonchenkoc

a Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Av. Diagonal 647, 08028 Barcelona, Spain
b Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, D-10623 Berlin, Germany
c Institute of Applied Mathematics and Cybernetics, Nizhny Novgorod University, pr. Gagarina 23, Nizhny Novgorod, 603950 Russia
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DOI: https://doi.org/10.1134/S1560354714060082
Abstract: We study bifurcations of nonorientable area-preserving maps with quadratic homoclinic tangencies. We study the case when the maps are given on nonorientable twodimensional surfaces. We consider one- and two-parameter general unfoldings and establish results related to the emergence of elliptic periodic orbits.
Keywords: area-preserving map, non-orientable surface, elliptic point, homoclinic tangency, bifurcation.
Funding agency Grant number
Russian Science Foundation 14-41-00044
14-12-00811
Russian Foundation for Basic Research 13-01-00589
13-01-97028-povolzhye
14-01-00344
Ministerio de Economía y Competitividad de España MTM2012-31714
Deutsche Forschungsgemeinschaft
Generalitat de Catalunya 2014SGR504
This work was partially supported by the Russian Scientific Foundation Grant 14-41- 00044. Section 3 was carried out by the RSF-grant (project No.14-12-00811). SG was partially supported by the grants of RFBR No.13-01-00589, 13-01-97028-povolzhye and 14-01-00344. AD and MG were partially supported by the Spanish MINECO-FEDER Grant MTM2012-31714 and the Catalan Grant 2014SGR504. MG was supported by the DFG Collaborative Research Center TRR 109 “Discretization in Geometry and Dynamics”.
Received: 30.09.2014
Accepted: 19.10.2014
Bibliographic databases:
Document Type: Article
MSC: 37C05, 37C29, 37E30, 37G25
Language: English
Citation: Amadeu Delshams, Marina Gonchenko, Sergey V. Gonchenko, “On Bifurcations of Area-preserving and Nonorientable Maps with Quadratic Homoclinic Tangencies”, Regul. Chaotic Dyn., 19:6 (2014), 702–717
Citation in format AMSBIB
\Bibitem{DelGonGon14}
\by Amadeu~Delshams, Marina Gonchenko, Sergey V. Gonchenko
\paper On Bifurcations of Area-preserving and Nonorientable Maps with Quadratic Homoclinic Tangencies
\jour Regul. Chaotic Dyn.
\yr 2014
\vol 19
\issue 6
\pages 702--717
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\crossref{https://doi.org/10.1134/S1560354714060082}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3284610}
\zmath{https://zbmath.org/?q=an:06507828}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000345996200008}
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