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ON THE CENTER CONDITIONS FOR ANALYTIC MONODROMIC DEGENERATE SINGULARITIES

JAUME GINÉ

Departament de Matemàtica, Universitat de Lleida, Av. Jaume II, 69. 25001 Lleida, Catalonia, Spain

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and

JAUME LLIBRE

Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain

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https://doi.org/10.1142/S0218127412503038Cited by:9 (Source: Crossref)

Abstract

In this paper, we present two methods for detecting centers of monodromic degenerate singularities of planar analytic vector fields. These methods use auxiliary symmetric vector fields and can be applied independently so that the singularity is algebraic solvable or not, or has characteristic directions or not. We remark that these are the first methods which allow to study monodromic degenerate singularities with characteristic directions.

Keywords:

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