复多项式向量场轨线的极限性态
Limiting behavior of trajectories of complex polynomial vector fields
摘要：
证明了复射影平面上多项式向量场的每条轨迹都累加到该向量场的奇异轨迹上。这个陈述代表了庞加莱-本迪克森定理的全纯版本，并解决了希尔伯特第16个问题的复解析对应。主要结果也可以重新表述为$\pp^2$上全纯叶理的“例外极小”的不存在性，特别地，它暗示了复射影平面上实解析Levi平坦超曲面的不存在性.最后，我们描述（在第一近似）的方式最小复杂的轨迹接近奇异轨迹的向量场。
英文摘要：
We prove that every trajectory of a polynomial vector field on the complex projective plane accumulates to the singular locus of the vector field. This statement represents a holomorphic version of the Poincare-Bendixson theorem and solves the complex analytic counterpart of Hilbert's 16th problem. The main result can be also reformulated as the nonexistence of "exceptional minimals" of holomorphic foliations on $\pp^2$ and, in particular, implies the nonexistence of real analytic Levi flat hypersurfaces in the complex projective plane. Finally, we describe (in the first approximation) the way a minimal complex trajectory approaches the singular locus of the vector field.
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