局部动力学中的闭不变集
On Closed Invariant Sets in Local Dynamics
摘要：
研究了$U,$的$f-$不变子集$\mathcal{C}$上全纯映射的动力学行为，其中$f:U \to \mathbb{C}^k.$研究了两种情形：当$U$是$\mathbb{C}^k$的开的、连通的多项式凸子集，且$\mathcal{C} \subset \subset U,$在$U,$中闭时，以及当$\partial U$具有p.s. h.本文的第二部分证明了多复变全纯映射的Birkhoff型定理，即给定定义在$\overline{U},$的邻域中的单射全纯映射$\mathcal{C}$，其中$U$是星形的，$f(U)$是Runge域，我们证明了存在唯一的、前向不变的、极大的、接触$\partial U.$的$\overline{U}$的紧连通子集
英文摘要：
We investigate the dynamical behaviour of a holomorphic map on a $f-$invariant subset $\mathcal{C}$ of $U,$ where $f:U \to \mathbb{C}^k.$ We study two cases: when $U$ is an open, connected and polynomially convex subset of $\mathbb{C}^k$ and $\mathcal{C} \subset \subset U,$ closed in $U,$ and when $\partial U$ has a p.s.h. barrier at each of its points and $\mathcal{C}$ is not relatively compact in $U.$ In the second part of the paper, we prove a Birkhoff's type Theorem for holomorphic maps in several complex variables, i.e. given an injective holomorphic map $f,$ defined in a neighborhood of $\overline{U},$ with $U$ star-shaped and $f(U)$ a Runge domain, we prove the existence of a unique, forward invariant, maximal, compact and connected subset of $\overline{U}$ which touches $\partial U.$
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。
