论文标题
理想的边界和积累引理
The ideal boundary and the accumulation lemma
论文作者
论文摘要
让$ s $成为可能具有边界的连接表面，有限的鲍勒级尺寸为$μ$，它在开放式套装上是阳性的，而$ f：s $ to s $ a同同态保存$μ$。我们证明，如果$ k $是$ s $的紧凑连接子集，而$ l $是双曲线周期性点的分支，则如果$ f $，则$ l \ cap k \ ne \ emptyset $ thement $ l \ l \ subset k $。这称为积累引理。为此，我们开发了一个具有边界的连接表面的分类，并表征紧凑型子集的残留域，其中有限许多连接的组件在带有边界的连接表面中。
Let $S$ be a connected surface possibly with boundary, $μ$ a finite Borel measure which is positive on open sets and $f:S\to S$ a homeomorphism preserving $μ$. We prove that if $K$ is a compact connected subset of $S$ and $L$ is a branch of a hyperbolic periodic point if $f$ then $L\cap K\ne\emptyset$ implies $L\subset K$. This is called the accumulation lemma. For this we develop a classification of connected surfaces with boundary and a characterization of residual domains of compact subsets with finitely many connected components in a connected surface with boundary.
