Geodesic
Branching of periodic orbits from Kukles isochrones
Electronic journal of differential equations, Tome 1998 (1998)
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.
Classification : 34C15, 34C25, 58F14, 58F21, 58F30
Keywords: limit cycles, isochronous system, linearization, perturbations 
@article{EJDE_1998__1998__a8,
     author = {Toni,  B.},
     title = {Branching of periodic orbits from {Kukles} isochrones},
     journal = {Electronic journal of differential equations},
     year = {1998},
     volume = {1998},
     zbl = {0899.34027},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a8/}
}
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%A Toni,  B.
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%J Electronic journal of differential equations
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Toni,  B. Branching of periodic orbits from Kukles isochrones. Electronic journal of differential equations, Tome 1998 (1998). http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a8/