Simultaneous linearization and centralizers of parabolic self-maps I: zero hyperbolic step

Manuel D. Contreras, Santiago Díaz-Madrigal, Pavel Gumenyuk

Let $\phi :\mathbb{D}\to \mathbb{D}$ be a parabolic self-map of the unit disc $\mathbb{D}$ having zero hyperbolic step. We study holomorphic self-maps of $\mathbb{D}$ commuting with $\phi$.…