Characterization of isochronous foci for planar analytic differential systems

Jaume Giné; Maite Grau

doi:10.1017/S0308210500004236

Abstract

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We consider the two-dimensional autonomous systems of differential equations of the form where P(x,y) and Q(x,y) are analytic functions of order greater than or equal to 2. These systems have a focus at the origin if λ ≠ 0, and have either a centre or a weak focus if λ = 0. In this work we study the necessary and sufficient conditions for the existence of an isochronous critical point at the origin. Our result is, to the best of our knowledge, original when applied to weak foci and gives known results when applied to strong foci or to centres.

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Characterization of isochronous foci for planar analytic differential systems

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