Normal forms and linearization of holomorphic dilation type semigroups in several variables

Linearization models for parabolic dynamical systems via Abel's functional equation

We study linearization models for continuous one-parameter semigroups of parabolic type. In particular, we introduce new limit schemes to obtain solutions of Abel's functional equation and to study asymptotic behavior of such semigroups. The crucial point is that these solutions are univalent functions convex in one direction. In a parallel direction, we find analytic conditions which determine certain geometric properties of those functions, such as the location of their images in either a half-plane or a strip, and their containing either a half-plane or a strip. In the context of semigroup …

抛物自映射的同时线性化与中心化子II：正双曲步长

Simultaneous linearization and centralizers of parabolic self-maps II: positive hyperbolic step

研究单位圆盘正双曲步长抛物自映射的交换性、同时线性化和全纯模型关系，得到交换对同时线性化的存在唯一性结果，还表明特定族可与\(\varphi\)同时线性化当且仅当族中元素两两交换，扩展了Cowen相关结果。

Non-commutative holomorphic semicocycles

This paper studies holomorphic semicocycles over semigroups in the unit disk, which take values in an arbitrary unital Banach algebra. We prove that every such semicocycle is a solution to a corresponding evolution problem. We then investigate the linearization problem: which semicocycles are cohomologous to constant semicocycles? In contrast with the case of commutative semicocycles, in the non-commutative case non-linearizable semicocycles are shown to exist. Simple conditions for linearizability are derived and are shown to be sharp.

抛物自映射的同时线性化与中心化 I：零超几何步骤

Simultaneous linearization and centralizers of parabolic self-maps I: zero hyperbolic step

本文研究了抛物自映射的同时线性化与中心化问题，证明了与抛物自映射相容的全纯自映射的条件，并展示了中心化半群的可交换性及单值性性质。