论文标题
非分类近核代谢重归于
Non-degenerate near-parabolic renormalization
论文作者
论文摘要
事实证明，在抛物线和近羟基重质重质化下不变类对于研究多项式动力学非常有用。 Inou-Shishikura引入了第一类，以研究二次多项式。他们的论点已扩展到Chéritat和Yang的单义立方案件。但是，所有这些类仅适用于具有乘数接近一个的固定点的地图，尽管众所周知，当乘数接近任何统一根时，也会发生类似的现象。在本文中，我们在一般环境中定义了抛物线和近羟基蛋白酶的重新归一化操作员，并构建不变类。此外，我们比较当一个统一的根部接近另一个核心时，相应的近核酸重归于。
Invariant classes under parabolic and near-parabolic renormalization have proved extremely useful for studying the dynamics of polynomials. The first such class was introduced by Inou-Shishikura to study quadratic polynomials; their argument has been extended to the unicritical cubic case by Chéritat and Yang. However, all of these classes are only applicable to maps which have a fixed point with multiplier close to one, though it is well-known that similar phenomena occur when the multiplier is close to any root of unity. In this paper we define the parabolic and near-parabolic renormalization operators in the general setting and construct invariant classes. Additionally, we compare the corresponding near-parabolic renormalizations when one root of unity is close to another.
