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Séminaire du LJLL - 24 02 2017 14h00 : J. Llibre
Jaume Llibre (Université Autonome de Barcelone)
The center-focus problem, the integrability of the centers, and the divergence
Abstract
We shall recall briefly how can be the local phase portraits of the equilibrium points of an analytic differential system in the plane, and we shall put our attention in the center-focus problem, i.e. how to distinguish a center from a focus. This is a difficult problem which is not completely solved. We shall provide some new results about the local integrability of the centers and on the problem of distinguishing one focus from a center using the divergence of the differential system.