Article ID Journal Published Year Pages File Type
4610436 Journal of Differential Equations 2014 21 Pages PDF
Abstract

In this paper we consider analytic planar differential systems having a first integral of the form H(x,y)=A(x)+B(x)y+C(x)y2H(x,y)=A(x)+B(x)y+C(x)y2 and an integrating factor κ(x)κ(x) not depending on y. Our aim is to provide tools to study the period function of the centers of this type of differential system and to this end we prove three results. Theorem A gives a characterization of isochronicity, a criterion to bound the number of critical periods and a necessary condition for the period function to be monotone. Theorem B is intended for being applied in combination with Theorem A in an algebraic setting that we shall specify. Finally, Theorem C is devoted to study the number of critical periods bifurcating from the period annulus of an isochrone perturbed linearly inside a family of centers. Four different applications are given to illustrate these results.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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