Simultaneous Linearization of Holomorphic Maps with Hyperbolic and Parabolic Fixed Points

Tetsuo Ueda
2008 Publications of the Research Institute for Mathematical Sciences  
We study local holomorphic mappings of one complex variable with parabolic fixed points as a limit of a families of mappings with attracting fixed points. We show that the Fatou coordinate for a parabolic fixed point can be obtained as a limit of some linear function of the solutions to Schröder equation for perturbed mappings with attracting fixed points.
doi:10.2977/prims/1207921077 fatcat:d3uppzyxhbbizbd2gmiheqqzte