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arXiv · 1607.04555

Simultaneous models for commuting holomorphic self-maps of the ball

Leandro Arosio·Filippo Bracci
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Abstract

We prove that a finite family of commuting holomorphic self-maps of the unit ball $\mathbb{B}^q\subset \mathbb{C}^q$ admits a simultaneous holomorphic conjugacy to a family of commuting automorphisms of a possibly lower dimensional ball, and that such conjugacy satisfies a universal property. As an application we describe when a hyperbolic and a parabolic holomorphic self-map of $\mathbb{B}^q$ can commute.

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Leandro Arosio, Filippo Bracci. 2016-07-15. Simultaneous models for commuting holomorphic self-maps of the ball. https://arxiv.org/abs/1607.04555

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