A codimension 2 Bifurcation for reversible Vector Fields

Abstract : For a family of reversible vector fields having a fixed point at the origin, we present the problem where , at criticality, the derivative at the origin has a multiple 0 eigenvalue with a 4 x 4 Jordan block. This is a codimension 2 singularity for reversible vector fields. This case happens in the water-wave problem for Bond number 1/3 and Froude number 1. We study the persistence of all known phenomena on the codimension one curves (in the parameter plane), especially concerning homoclinic orbits. One of these unfoldings is the 1:1 resonance Hopf bifurcation. The study strongly relies upon the knowledge of the reversible normal forms associated with the 4 X 4 Jordan block, and the unfolded situations , together with appropriate scalings.
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Article dans une revue
Fields Institute Communications, Springer, 1995, 4, pp.17
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https://hal.univ-cotedazur.fr/hal-01271013
Contributeur : Gerard Iooss <>
Soumis le : mardi 9 février 2016 - 15:08:46
Dernière modification le : jeudi 3 mai 2018 - 13:32:58

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  • HAL Id : hal-01271013, version 1

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Gérard Iooss. A codimension 2 Bifurcation for reversible Vector Fields. Fields Institute Communications, Springer, 1995, 4, pp.17. 〈hal-01271013〉

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