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Regular and Chaotic Dynamics

, Volume 19, Issue 4, pp 461–473 | Cite as

On bifurcations of multidimensional diffeomorphisms having a homoclinic tangency to a saddle-node

  • Serey V. GonchenkoEmail author
  • Olga V. Gordeeva
  • Valery I. Lukyanov
  • Ivan I. Ovsyannikov
Article

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 

MSC2010 numbers

37C05 34C37 37C29 37G25 

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Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  • Serey V. Gonchenko
    • 1
    Email author
  • Olga V. Gordeeva
    • 1
  • Valery I. Lukyanov
    • 1
  • Ivan I. Ovsyannikov
    • 1
    • 2
  1. 1.Nizhny Novgorod State UniversityNizhny NovgorodRussia
  2. 2.Imperial CollegeLondonUK

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