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arXiv · 2002.05399

Canonical models on strongly convex domains via the squeezing function

Amedeo Altavilla·Leandro Arosio·Lorenzo Guerini
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Abstract

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.

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Amedeo Altavilla, Leandro Arosio, Lorenzo Guerini. 2020-06-22. Canonical models on strongly convex domains via the squeezing function. https://doi.org/10.1007/s12220-020-00448-5

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