论文标题
在表面上复杂矢量场的真实中心奇点上
On real center singularities of complex vector fields on surfaces
论文作者
论文摘要
经典的Lyapunov-Poincaré中心定理的各种版本之一指出，非排定实际分析中心类型的平面矢量场奇异性是分析性的第一积分。为了证明这一结果，R。Moussu建立了这种结果与全态叶子奇异性（\ cite {Moussu}）之间的重要联系。在本文中，我们考虑了两个主要框架的概括：（i）平面真实的分析矢量场，其奇异性附近具有“许多”周期性轨道，并且（ii）霍明型叶子的细菌在二维二维中具有合适的奇异性。在本文中，我们证明了Poincaré-Lyapunov Center定理的版本，包括Holomorthic Vector Fields。我们还提供了一些应用程序，暗示在此框架中还有更多探索。
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 singularity and (ii) germs of holomorphic foliations having a suitable singularity in dimension two. In this paper we prove versions of Poincaré-Lyapunov center theorem, including for the case of holomorphic vector fields. We also give some applications, hinting that there is much more to be explored in this framework.
