Electronic Journal of Differential Equations,
Vol. 1998(1998), No. 13, pp. 1-10.

Title: Branching of periodic orbits from Kukles isochrones

Author: B. Toni (Univ. Autonoma, Morelos, Mexico.)

Abstract: 
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.