论文标题
分析性Hopf-Zero奇异性中的杂斜连接的分解：Stokes常数的严格计算
Breakdown of heteroclinic connections in the analytic Hopf-Zero singularity: Rigorous computation of the Stokes constant
论文作者
论文摘要
考虑三维保守的Hopf-Zero奇异性的分析通用展开。在确定奇异性的参数的开放条件下，当展开参数足够小时，展开具有两个鞍座。其中一个具有一维稳定的歧管和二维不稳定的歧管，而另一个具有一维不稳定的歧管和二维稳定的歧管。 Baldomá，Castejón和Seara [BCS13]给出了适当的横截面中一维不变歧管之间距离的渐近公式。相对于扰动参数，该距离成倍小，这取决于通常称为stokes常数的距离。该常数的非变化意味着该部分处的不变歧管之间的距离不是零。但是，到目前为止，还不存在分析技术来检查该条件。在本文中，我们提供了一种用于获得Stokes常数准确的严格计算机辅助边界的方法。我们将其应用于Hopf-Zero奇异性的两个具体展开，获得了计算机辅助证明该常数为非零的证据。
Consider analytic generic unfoldings of the three dimensional conservative Hopf-Zero singularity. Under open conditions on the parameters determining the singularity, the unfolding possesses two saddle-foci when the unfolding parameter is small enough. One of them has one dimensional stable manifold and two dimensional unstable manifold whereas the other one has one dimensional unstable manifold and two dimensional stable manifold. Baldomá, Castejón and Seara [BCS13] gave an asymptotic formula for the distance between the one dimensional invariant manifolds in a suitable transverse section. This distance is exponentially small with respect to the perturbative parameter, and it depends on what is usually called a Stokes constant. The non-vanishing of this constant implies that the distance between the invariant manifolds at the section is not zero. However, up to now there do not exist analytic techniques to check that condition. In this paper we provide a method for obtaining accurate rigorous computer assisted bounds for the Stokes constant. We apply it to two concrete unfoldings of the Hopf-Zero singularity, obtaining a computer assisted proof that the constant is non-zero.
