Period function for perturbed isochronous centres

Emilio Freire, Armengol Gasull, Antoni Guillamon

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Resum

The problems related to the Poincaré map often exhibit a similar formulation in terms of the time (or period) function associated to a continuum of periodic orbits. In this paper, parallel to the Melnikov method used to study the periodic orbits that persist after a perturbation of a centre, we present an intrinsic general formula for the derivative of the period function. This formula is obtained by exploiting the Lie symmetries of a planar vector field X having an isochronous centre, and it is applied to estimate the number of critical periods of a "close" vector field X∈ = X + ∈Y having a centre.
Idioma originalEnglish
Pàgines (de-a)275-284
RevistaQualitative Theory of Dynamical Systems
Volum3
DOIs
Estat de la publicacióPublicada - 1 de des. 2002

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