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Regular and Chaotic Dynamics

, Volume 14, Issue 1, pp 116–136 | Cite as

On cascades of elliptic periodic points in two-dimensional symplectic maps with homoclinic tangencies

  • M. S. GonchenkoEmail author
  • S. V. Gonchenko
Jürgen Moser-80

Abstract

We study bifurcations of two-dimensional symplectic maps with quadratic homoclinic tangencies and prove results on the existence of cascade of elliptic periodic points for one and two parameter general unfoldings.

Key words

symplectic map homoclinic tangency bifurcation generic elliptic point KAM-theory 

MSC2000 numbers

37C29 37G25 37J10 37J20 

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Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  1. 1.Departament de Matemàtica Aplicada IUniversitat Politècnica de CatalunyaBarcelonaSpain
  2. 2.Research Institute of Applied Mathematics and CyberneticsNizhny Novgorod State University 10Nizhny NovgorodRussia

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