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

Canonical models on strongly convex domains via the squeezing function

Amedeo Altavilla;
2020

Abstract

We prove that if a holomorphic self-map $fcolon Omega o Omega$ of a bounded strongly convex domain $Omegasubset mathbb C^q$ 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 $fcolon Omega o Omega$ with a boundary repelling fixed point. Both results are obtained by rescaling the dynamics of $f$ via the squeezing function.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11586/265192
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