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The Real Period Function of A3 Singularity and Perturbations of the Spherical Pendulum

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Compositio Mathematica

Abstract

We prove that the Hessian matrix of the real period function ψ(λ) associated with the real versal deformation f λ(x)=±x 4+λ2 x 2+λ1 x+λ0 of a singularity of type A 3, is nondegenerate, provided that λεℝ3 does not belong to the discriminant set of the singularity. We explain the relation between this result and the perturbations of the spherical pendulum.

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Authors and Affiliations

  1. Laboratoire Emile Picard, UMR 5580, Université Paul Sabatier, 118, route de Narbonne, 31062, Toulouse Cedex, France

    Lubomir Gavrilov & Olivier Vivolo

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  1. Lubomir Gavrilov
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  2. Olivier Vivolo
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Gavrilov, L., Vivolo, O. The Real Period Function of A3 Singularity and Perturbations of the Spherical Pendulum. Compositio Mathematica 123, 167–184 (2000). https://doi.org/10.1023/A:1001821300769

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