2022
DOI: 10.21203/rs.3.rs-1954602/v1
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On real center singularities of complex vector fields on surfaces

Abstract: One of the various versions of the classical Lyapunov-Poincaré center theorem states that a nondegenerate real analytic center type planar vector field singularity admits an analytic first integral. In a more proof of this result, R. Moussu establishes important connection between this result and the theory of singularities of holomorphic foliations (\cite{moussu}). In this paper we consider generalizations for two main frameworks: (i) planar real analytic vector fields with ``many'' periodic orbits near the s… Show more

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