Canonical models on strongly convex domains via the squeezing function

Abstract

We prove that if a holomorphic self-map $f:\Omega \to \Omega$ of a bounded strongly convex domain $\Omega \subset {\mathbb{C}}^q$ 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 $f:\Omega \to \Omega$ with a boundary repelling fixed point. Both results are obtained by rescaling the dynamics of $f$ via the squeezing function.

Cited by in corpus (2)

• The horofunction boundary of a Gromov hyperbolic space
• Backward dynamics of non-expanding maps in Gromov hyperbolic metric spaces