Results in Mathematics

, Volume 21, Issue 1–2, pp 211–223

Bifurcation of degenerate homoclinics

  • André Vanderbauwhede

DOI: 10.1007/BF03323080

Cite this article as:
Vanderbauwhede, A. Results. Math. (1992) 21: 211. doi:10.1007/BF03323080


We analyze the continuation and bifurcation of homoclinic orbits near a given degenerate homoclinic orbit. We show that the existence of such degenerate homoclinic orbit is a codimension three phenomenon, and that generically the set of parametervalues at which a nearby homoclinic exists forms a codimension one surface which shows a singularity of Whitney umbrella type at the critical parametervalue. The line of self-intersecting points of such surface corresponds to systems which have two nearby homoclinics.

Copyright information

© Birkhäuser Verlag, Basel 1992

Authors and Affiliations

  • André Vanderbauwhede
    • 1
  1. 1.Instituut voor Theoretische MechanicaUniversiteit GentGentBelgium

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