论文标题
通过挤压功能强烈凸起域上的规范模型
Canonical models on strongly convex domains via the squeezing function
论文作者
论文摘要
We prove that if a holomorphic self-map $f\colon Ω\to Ω$ of a bounded strongly convex domain $Ω\subset \mathbb C^q$ with smooth boundary is hyperbolic then it admits a natural semi-conjugacy with a hyperbolic automorphism of a possibly lower dimensional ball $\mathbb B^k$.我们还获得了带有边界驱动固定点的全体形态自图$ f \ colonω\ toω$的双重结果。这两种结果均通过通过挤压功能重新缩放$ f $的动力学来获得。
We prove that if a holomorphic self-map $f\colon Ω\to Ω$ of a bounded strongly convex domain $Ω\subset \mathbb C^q$ with smooth boundary is hyperbolic then it admits a natural semi-conjugacy with a hyperbolic automorphism of a possibly lower dimensional ball $\mathbb B^k$. We also obtain the dual result for a holomorphic self-map $f\colon Ω\to Ω$ with a boundary repelling fixed point. Both results are obtained by rescaling the dynamics of $f$ via the squeezing function.
