The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems

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2006
Author
Giacomini, Héctor
Giné, Jaume
Llibre, Jaume
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Abstract
In this work we study the centers of planar analytic vector fields which are limit of linear type centers. It is proved that all the nilpotent centers are limit of linear type centers and consequently the Poincaré–Liapunov method to find linear type centers can be also used to find the nilpotent centers.
Moreover, we show that the degenerate centers which are limit of linear type centers are also detectable with the Poincaré–Liapunov method.
URI
http://hdl.handle.net/10459.1/57797
DOI
https://doi.org/10.1016/j.jde.2006.03.012
Is part of
Journal of Differential Equations, 2006, vol. 227, núm. 2, p. 406-426
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