Journal of Dynamics and Differential Equations

, Volume 12, Issue 4, pp 807–850 | Cite as

Resonant Homoclinic Flip Bifurcations

  • Ale Jan Homburg
  • Bernd Krauskopf


This paper studies three-parameter unfoldings of resonant orbit flip and inclination flip homoclinic orbits. First, all known results on codimension-two unfoldings of homoclinic flip bifurcations are presented. Then we show that the orbit flip and inclination flip both feature the creation and destruction of a cusp horseshoe. Furthermore, we show near which resonant flip bifurcations a homoclinic-doubling cascade occurs. This allows us to glue the respective codimension-two unfoldings of homoclinic flip bifurcations together on a sphere around the central singularity. The so obtained three-parameter unfoldings are still conjectural in part but constitute the simplest, consistent glueings.

homoclinic bifurcation inclination flip orbit flip homoclinic-doubling cascade cusp horseshoe 


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Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • Ale Jan Homburg
    • 1
  • Bernd Krauskopf
    • 2
  1. 1.Institut für Mathematik IFreie Universität BerlinBerlinGermany
  2. 2.Engineering MathematicsUniversity of BristolBristolUnited Kingdom

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