Holomorphic self-maps of the disk intertwining two linear fractional maps
Holomorphic self-maps of the disk intertwining two linear fractional maps
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 detailed analysis of the solutions of Schroeder's and Abel's equations.In particular, we characterize the maps that commute with a given …