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.
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”.
\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}
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Linking options:
https://www.mathnet.ru/eng/rcd193
https://www.mathnet.ru/eng/rcd/v19/i6/p702
This publication is cited in the following 2 articles:
Muni S.Sh., McLachlan I R., Simpson D.J.W., “Homoclinic Tangencies With Infinitely Many Asymptotically Stable Single-Round Periodic Solutions”, Discret. Contin. Dyn. Syst., 41:8 (2021), 3629–3650
A. Delshams, M. Gonchenko, S. Gonchenko, “Corrigendum: On dynamics and bifurcations of area-preserving maps with homoclinic tangencies (2015 Nonlinearity 28 3027)”, Nonlinearity, 30:3 (2017), c2
Citation in format AMSBIB
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