Revista Matemática Iberoamericana

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Volume 24, Issue 3, 2008, pp. 765–824
DOI: 10.4171/RMI/556

Published online: 2008-12-31

The linear fractional model on the ball

Frédéric Bayart[1]

(1) Université Blaise Pascal, Aubière, France

Given a holomorphic self-map $\varphi$ of the ball of $\mathbb{C}^N$, we study whether there exists a map $\sigma$ and a linear fractional transformation $A$ such that $\sigma\circ\varphi=A\circ\sigma$. This is an important result when $N=1$ with a great number of applications. We extend this result to the multi-dimensional setting for a large class of maps. Applications to commuting holomorphic self-maps are given.

Keywords: Linear fractional maps, iteration

Bayart Frédéric: The linear fractional model on the ball. Rev. Mat. Iberoamericana 24 (2008), 765-824. doi: 10.4171/RMI/556