带蛛网的Poincaré函数
Poincaré functions with spiders' webs
摘要：
对于具有排斥不动点w的多项式p，我们考虑p在w处的庞加莱函数，即对于复平面中的所有z，满足L（0）=w和p（L（z））=L（p '（w）*z）的整函数L。我们证明，如果p的包含w的朱利亚集的分量等于{w}，则L的（快速）逃逸集是一个蜘蛛网;特别是它是连通的。更确切地说，我们分类的所有线性化的多项式关于蜘蛛网结构的所有点的集合逃脱速度比迭代的最大模函数在一个足够大的点。
英文摘要：
For a polynomial p with a repelling fixed point w, we consider Poincaré functions of p at w, i.e. entire functions L which satisfy L(0)=w and p(L(z))=L(p'(w)*z) for all z in the complex plane. We show that if the component of the Julia set of p that contains w equals {w}, then the (fast) escaping set of L is a spider's web; in particular it is connected. More precisely, we classify all linearizers of polynomials with regards to the spider's web structure of the set of all points which escape faster than the iterates of the maximum modulus function at a sufficiently large point.
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