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Parametric normal forms for Bogdanov--Takens singularity; the generalized saddle-node case

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  • We obtain a parametric (and an orbital) normal form for any non-degenerate perturbation of the generalized saddle-node case of Bogdanov--Takens singularity. Explicit formulas are derived and greatly simplified for an efficient implementation in any computer algebra system. A Maple program is prepared for an automatic parametric normal form computation. A section is devoted to present some practical formulas which avoid technical details of the paper.
    Mathematics Subject Classification: Primary: 34C20; Secondary: 34A34, 16W50.


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