The linear fractional model on the ball
Rev. Mat. Iberoamericana, Tome 24 (2008) no. 2, p. 765-824 / Harvested from Project Euclid
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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.
Publié le : 2008-04-15
Classification:  linear fractional maps,  iteration,  32H50,  32A10 
@article{1228834294,
     author = {Bayart
,  
Fr\'ed\'eric},
     title = {The linear fractional model on the ball},
     journal = {Rev. Mat. Iberoamericana},
     volume = {24},
     number = {2},
     year = {2008},
     pages = { 765-824},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1228834294}
}

Bayart
,  
Frédéric. The linear fractional model on the ball. Rev. Mat. Iberoamericana, Tome 24 (2008) no. 2, pp.  765-824. http://gdmltest.u-ga.fr/item/1228834294/