论文标题
一类多项式图及其应用
The parabolic and near-parabolic renormalization for a class of polynomial maps and its applications
论文作者
论文摘要
对于一类带有抛物线固定点和大于$ 21 $的变量的多项式图，基于FATOU坐标和号角图引入了抛物线的重新归一化，并且还给出了在抛物线重质重新分配下不变的地图。对于这些地图的微小扰动，还基于基本区域定义的第一个返回地图引入了近抛蛋白的重新归一化。作为应用程序，我们显示了大于$ 21 $的学位的不可鉴定的多项式图的存在，因此朱莉娅集合具有正面的lebesgue措施和Cremer固定点，这为经典的Fatou构想（带有正面的朱利娅（Julia）的存在带有正面区域的存在）提供了积极的答案，其学位大于21美元。
For a class of polynomial maps of one variable with a parabolic fixed points and degrees bigger than $21$, the parabolic renormalization is introduced based on Fatou coordinates and horn maps, and a type of maps which are invariant under the parabolic renormalization is also given. For the small perturbation of these kinds of maps, the near-parabolic renormalization is also introduced based on the first return maps defined on the fundamental regions. As an application, we show the existence of non-renormalizable polynomial maps with degrees bigger than $21$ such that the Julia sets have positive Lebesgue measure and Cremer fixed points, this provides a positive answer for the classical Fatou conjecture (the existence of Julia set with positive area) with degrees bigger than $21$.
