穿孔平面上有界型超越自映射的动态射线
Dynamic rays of bounded-type transcendental self-maps of the punctured plane
摘要：
研究了$\mathcal B^*$类中函数的逃逸集，即零和无穷大都是本质奇点的全纯函数$f:\mathbb C^*\to\mathbb C^*$，且$f$的奇异值集包含在$\mathbb C^*$的紧致环中.对于$\mathcal B^*$类中的函数，转义点位于其Julia集中。如果$f$是$\mathbb C^*$的有限阶超越自映射的合成（因此，在类$\mathcal B^*$中），那么我们证明了$f$的每个逃逸点都可以通过一致逃逸点的曲线连接到本质奇点之一.此外，对于每一个基本的行程$e\in\{0,\infty\}^\mathbb N$，我们表明，逃逸集$f$包含一个康托花束的曲线，积累到$\{0,\infty\}$根据$e$迭代下由$f$。
英文摘要：
We study the escaping set of functions in the class $\mathcal B^*$, that is, holomorphic functions $f:\mathbb C^*\to\mathbb C^*$ for which both zero and infinity are essential singularities, and the set of singular values of $f$ is contained in a compact annulus of $\mathbb C^*$. For functions in the class $\mathcal B^*$, escaping points lie in their Julia set. If $f$ is a composition of finite order transcendental self-maps of $\mathbb C^*$ (and hence, in the class $\mathcal B^*$), then we show that every escaping point of $f$ can be connected to one of the essential singularities by a curve of points that escape uniformly. Moreover, for every essential itinerary $e\in\{0,\infty\}^\mathbb N$, we show that the escaping set of $f$ contains a Cantor bouquet of curves that accumulate to $\{0,\infty\}$ according to $e$ under iteration by $f$.
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