论文标题
三维实际流量I：拟合域的分层
Stratification of three-dimensional real flows I: Fitting Domains
论文作者
论文摘要
让$ξ$为$ \ mathbb {r}^3 $中的一个分析矢量字段，其起点是孤立的，并且在降低奇异性$π$π之后仅具有双曲线奇异点。图像的结合由$λ$表示的那些双曲线点的本地不变歧管的$π$组成，由$ξ$累积至$ 0 \ in \ mathbb {r}^3 $组成。假设$π$的除数没有周期或一致的循环，以及莫尔斯 - 梅尔类型的特性，并且在这些时刻的特征值上没有谐音条件，在本文中，我们证明了$ \ {v_n \}的基本系统$ \ {v_n \} $ fordy forther fortier $ n of the Local $ nocal $;切入到$ξ$，除了$ fr（v_n）\capλ$，其中是强制性的。
Let $ξ$ be an analytic vector field in $\mathbb{R}^3$ with an isolated singularity at the origin and having only hyperbolic singular points after a reduction of singularities $π:M\to\mathbb{R}^3$. The union of the images by $π$ of the local invariant manifolds at those hyperbolic points, denoted by $Λ$, is composed of trajectories of $ξ$ accumulating to $0 \in \mathbb{R}^3$. Assuming that there are no cycles nor polycycles on the divisor of $π$, together with a Morse-Smale type property and a non-resonance condition on the eigenvalues at these points, in this paper we prove the existence of a fundamental system $\{V_n\}$ of neighborhoods well adapted for the description of the local dynamics of $ξ$: the frontier $Fr(V_n)$ is everywhere tangent to $ξ$ except around $Fr(V_n)\capΛ$, where transvesality is mandatory.
