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On Bifurcations of Homoclinic Tangencies in Area-Preserving Maps on Non-orientable Manifolds

  • Amadeu Delshams
  • Marina GonchenkoEmail author
  • Sergey Gonchenko
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 180)

Abstract

We study bifurcations of non-orientable area-preserving maps with quadratic homoclinic tangencies. We study the case when the maps are given on non-orientable two-dimensional manifolds. We consider one and two parameter general unfoldings and establish results related to the appearance of elliptic periodic orbits.

Keywords

Bifurcation Homoclinic tangency Area-preserving map Non-orientable Elliptic orbit 

Notes

Acknowledgments

The authors thank D.Turaev, L.Lerman and R.Ortega for fruitful discussions and remarks. This work has been partially supported by the Russian Scientific Foundation Grant 14-41-00044. S.G. has been supported partially by the grants of RFBR No.16-01-00324 and 14-01-00344. A.D. and M.G. have been partially supported by the Spanish MINECO-FEDER Grant MTM2012- 31714 and the Catalan Grant 2014SGR504.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Amadeu Delshams
    • 1
  • Marina Gonchenko
    • 1
    Email author
  • Sergey Gonchenko
    • 2
  1. 1.Departament de Matemàtica Aplicada IUniversitat Politècnica de CatalunyaBarcelonaSpain
  2. 2.Institute of Applied Mathematics and CyberneticsNizhny Novgorod UniversityNizhny NovgorodRussia

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