Mitchell, Zachary Thomas (2019-11). Fatou-Bieberbach Domains: A New Construction and a Theme on the Runge Property. Doctoral Dissertation. Thesis uri icon


  • Fatou-Bieberbach domains are a phenomenon specific to several complex variables. Techniques for producing such domains are limited and fundamental questions about containment between two Fatou-Bieberbach are still being raised. We show that given a countable collection of Runge Fatou-Bieberbach domains with a ball in common and a common point omitted, there exists a Runge Fatou-Bieberbach domain that contains the union. Additionally, we provide a new construction for Fatou-Bieberbach domains modelled on the attracting basin, using right-side composition instead of the prototypical left-side composition. We use this construction to show that there exists a strictly decreasing family of Fatou-Bieberbach domains whose intersection contains a Fatou-Bieberbach domain. Additionally, we provide a generalized condition for constructing attracting basins from a sequence of automorphisms.

publication date

  • November 2019