Holomorphic self-maps of the disk intertwining two linear fractional maps (Q2906469)

In this paper under review, the authors characterize the holomorphic self-maps of the unit disk that intertwine two given linear fractional self-maps of the disk. Their proofs are based on iteration and a detailed analysis of the Denjoy-Wolff points. In particular, the authors characterize the maps that commute with a given linear fractional map, and as an application they determine all roots of such maps in the sense of iteration. This also yields 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.NEWLINENEWLINEFor the entire collection see [Zbl 1232.30005].