Results in Mathematics

, Volume 21, Issue 1, pp 211–223

Bifurcation of degenerate homoclinics


  • André Vanderbauwhede
    • Instituut voor Theoretische MechanicaUniversiteit Gent

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