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Bifurcation of degenerate homoclinics

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Abstract

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.

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Authors and Affiliations

  1. Instituut voor Theoretische Mechanica, Universiteit Gent, Krijgslaan 281, B-9000, Gent, Belgium

    André Vanderbauwhede

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  1. André Vanderbauwhede
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Dedicated to Professor H.W. Knobloch on the occasion of his 65th birthday

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Vanderbauwhede, A. Bifurcation of degenerate homoclinics. Results. Math. 21, 211–223 (1992). https://doi.org/10.1007/BF03323080

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  • DOI: https://doi.org/10.1007/BF03323080

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