论文标题
单位光盘的单价自图的半群
Semigroup-fication of univalent self-maps of the unit disc
论文作者
论文摘要
令$ f $是单位光盘的单价自动图。我们介绍了一种称为{\ sl semogroup-ficric}的技术，该技术允许构建一个连续的semigroup $（ϕ_t）$的单位光盘的holomorphic自图的$，从某种意义上说，一个时间地图$ ϕ_1 $是非常接近$ f $。 $ f $的半元素与$ f $（椭圆形，双曲线，抛物线的抛物线或零步的抛物面）相同，并且在带有给定乘数的$ f $的边界常规固定点之间有一对一的对应关系，与给定的乘数集和$ ϕ_1 $的相应集合。此外，如果$ f $（因此$ ϕ_1 $）没有内部固定点，则轨道的斜率汇聚到Denjoy-Wolff点是相同的。该构建基于尸体形态模型，定位技术和Gromov双曲线。作为这种结构的应用，我们证明在非椭圆形的情况下，$ f $的轨道在且仅当$ f $的koenigs域与垂直线相对于$ f $的koenigs域是“几乎对称的”时，将$ f $的轨道非限制为Denjoy-Wolff点。
Let $f$ be a univalent self-map of the unit disc. We introduce a technique, that we call {\sl semigroup-fication}, which allows to construct a continuous semigroup $(ϕ_t)$ of holomorphic self-maps of the unit disc whose time one map $ϕ_1$ is, in a sense, very close to $f$. The semigrup-fication of $f$ is of the same type as $f$ (elliptic, hyperbolic, parabolic of positive step or parabolic of zero step) and there is a one-to-one correspondence between the set of boundary regular fixed points of $f$ with a given multiplier and the corresponding set for $ϕ_1$. Moreover, in case $f$ (and hence $ϕ_1$) has no interior fixed points, the slope of the orbits converging to the Denjoy-Wolff point is the same. The construction is based on holomorphic models, localization techniques and Gromov hyperbolicity. As an application of this construction, we prove that in the non-elliptic case, the orbits of $f$ converge non-tangentially to the Denjoy-Wolff point if and only if the Koenigs domain of $f$ is "almost symmetric" with respect to vertical lines.
