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November, 2008 The linear fractional model on the ball
Frédéric Bayart
Rev. Mat. Iberoamericana 24(3): 765-824 (November, 2008).


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.


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Frédéric Bayart . "The linear fractional model on the ball." Rev. Mat. Iberoamericana 24 (3) 765 - 824, November, 2008.


Published: November, 2008
First available in Project Euclid: 9 December 2008

zbMATH: 1165.32009
MathSciNet: MR2490162

Primary: 32A10‎ , 32H50

Keywords: iteration , linear fractional maps

Rights: Copyright © 2008 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.24 • No. 3 • November, 2008
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