Electron. J. Diff. Eqns., Vol. 1998(1998), No. 13, pp. 1-10.

Branching of periodic orbits from Kukles isochrones

B. Toni

We study local bifurcations of limit cycles from isochronous (or linearizable) centers. The isochronicity has been determined using the method of Darboux linearization, which provides a birational linearization for the examples that we analyze. This transformation simplifies the analysis by avoiding the complexity of the Abelian integrals appearing in other approaches. As an application of this approach, we show that the Kukles isochrone (linear and nonlinear) has at most one branch point of limit cycles. Moreover, for each isochrone, there are small perturbations with exactly one continuous family of limit cycles.

Submitted April 22, 1998. Published May 13, 1998.
Math Subject Classification: 34C15, 34C25, 58F14, 58F21, 58F30.
Key Words: Limit cycles, Isochronous system, Linearization, Perturbations.

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This article is related to another publication in the EJDE: Branching of periodic orbits from Kukles isochrones, by B. Toni, Vol. 1999(1999), No. 35, pp. 1-15

Bourama Toni
Facultad de Ciencias, Universidad Autonoma del Edo de Morelos
Cuernavaca 62210, Morelos, Mexico.
e-mail: toni@servm.fc.uaem.mx
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