论文标题
在带有周期性赫尔曼戒指的meromorthic功能的公式上
On the formulas of meromorphic functions with periodic Herman rings
论文作者
论文摘要
我们构建了一些理性图和超验药功能的明确公式，其赫尔曼（Herman）的月球严格大于一个时期。这给了Shishikura在1980年代提出的一个问题。此外，还发现了一些带有嵌套赫尔曼戒指的理性地图的公式。 为了获得具有周期性Herman环的先验性异晶函数的公式，一个关键的步骤是找到一个具有所有可能时期和旋转数量的Siegel磁盘的明确全部全部功能的族家族。这是基于证明相应参数空间中类似mandelbrot的周期一组的存在。
We construct some explicit formulas of rational maps and transcendental meromorphic functions having Herman rings of period strictly larger than one. This gives an answer to a question raised by Shishikura in the 1980s. Moreover, the formulas of some rational maps with nested Herman rings are also found. To obtain the formulas of transcendental meromorphic functions having periodic Herman rings, a crucial step is to find an explicit family of transcendental entire functions having bounded Siegel disks of all possible periods and rotation numbers. This is based on proving the existence of a Mandelbrot-like set of period one in the corresponding parameter space.
