Holomorphic self-maps of the disk intertwining two linear fractional maps
Dynamical Systems
2016-11-07 v2
Abstract
We characterize (in almost all cases) the holomorphic self-maps of the unit disk that intertwine two given linear fractional self-maps of the disk. The proofs are based on iteration and a careful analysis of the Denjoy-Wolff points. In particular, we characterize the maps that commute with a given linear fractional map (in the cases that are not already known) and, as an application, determine all "roots" of such maps in the sense of iteration (if any). This yields as a byproduct a short proof of a recent theorem on the embedding of a linear fractional transformation into a semigroup of holomorphic self-maps of the disk.
Cite
@article{arxiv.0806.2276,
title = {Holomorphic self-maps of the disk intertwining two linear fractional maps},
author = {Manuel D. Contreras and Santiago Díaz-Madrigal and María J. Martín and Dragan Vukotić},
journal= {arXiv preprint arXiv:0806.2276},
year = {2016}
}
Comments
This is a revised version