Simultaneous Linearization of Holomorphic Maps with Hyperbolic and Parabolic Fixed Points

Abstract

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 o with attracting fixed points.