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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
Affiliation:
Laboratoire Emile Picard, UMR 5580, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex, France. E-mail: [email protected]
Olivier Vivolo
Affiliation:
Laboratoire Emile Picard, UMR 5580, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex, France. E-mail: [email protected]
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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)=±x42x21x0 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.

Type
Research Article
Copyright
© 2000 Kluwer Academic Publishers