Period function for perturbed isochronous centres

Emilio Freire, Armengol Gasull, Antoni Guillamon

Research output: Contribution to journalArticleResearchpeer-review

15 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)275-284
JournalQualitative Theory of Dynamical Systems
Publication statusPublished - 1 Dec 2002


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