球面开子集上解析向量场Ω极限集的拓扑刻画
A topological characterization of the omega-limit sets of analytic vector fields on open subsets of the sphere
摘要：
在[15]中，V.Jimenez和J.Llibre刻画了球面和射影平面上解析向量场的Ω极限集，直到同胚。作者还研究了同样的问题，这些曲面的开子集。不幸的是，在他们的一般曲面方案中，一个重要的引理有一个缺口。虽然这个引理的证明可以在球面、平面、射影平面和射影平面减一点的情况下进行修改（因此[8]中对这些曲面的刻画是正确的），但这个引理并不普遍正确，参见[15]。因此，球面和射影平面的开子集上的解析向量场的拓扑刻画仍然是一个悬而未决的问题。在本文中，我们关闭这个问题的情况下，开放的子集的领域。
英文摘要：
In [15], V. Jimenez and J. Llibre characterized, up to homeomorphism, the omega limit sets of analytic vector fields on the sphere and the projective plane. The authors also studied the same problem for open subsets of these surfaces. Unfortunately, an essential lemma in their programme for general surfaces has a gap. Although the proof of this lemma can be amended in the case of the sphere, the plane, the projective plane and the projective plane minus one point (and therefore the characterizations for these surfaces in [8] are correct), the lemma is not generally true, see [15]. Consequently, the topological characterization for analytic vector fields on open subsets of the sphere and the projective plane is still pending. In this paper, we close this problem in the case of open subsets of the sphere.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
