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

Giacomini, Héctor; Giné, Jaume; Llibre, Jaume

doi:https://doi.org/10.1016/j.jde.2006.03.012

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Issue date

2006

Author

Giacomini, Héctor

Giné, Jaume

Llibre, Jaume

Suggested citation

Giacomini, Héctor; Giné, Jaume; Llibre, Jaume; . (2006) . The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems. Journal of Differential Equations, 2006, vol. 227, núm. 2, p. 406-426. https://doi.org/10.1016/j.jde.2006.03.012.

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