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

Published online by Cambridge University Press:  04 December 2007

Lubomir Gavrilov  and
Olivier Vivolo
Lubomir Gavrilov
Affiliation:
Laboratoire Emile Picard, UMR 5580, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex, France. E-mail: gavrilov@picard.ups-tlse.fr
Olivier Vivolo
Affiliation:
Laboratoire Emile Picard, UMR 5580, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex, France. E-mail: vivolo@picard.ups-tlse.fr
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Abstract

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We prove that the Hessian matrix of the real period function ψ(λ) associated with the real versal deformation fλ(x)=±x4+λ2x2+λ1x+λ0 of a singularity of type A3, is nondegenerate, provided that λ∈${\Bbb R}$3 does not belong to the discriminant set of the singularity. We explain the relation between this result and the perturbations of the spherical pendulum.

Keywords

elliptic integralKAM theoryspherical pendulum
Type
Research Article
Information
Compositio Mathematica , Volume 123 , Issue 2 , September 2000 , pp. 167 - 184
Copyright
© 2000 Kluwer Academic Publishers