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1 results

  • 14 - Finer Properties of Fatou Components

  • from Part III - Topological Dynamics of Meromorphic Functions
  • Janina Kotus, Warsaw University of Technology, Mariusz Urbański, University of North Texas
  • Book:
    Meromorphic Dynamics
    Published online:
    20 April 2023
    Print publication:
    04 May 2023, pp 67-84

  • Summary

    We analyze the structure of Fatou components and the structure of their boundaries in greater detail. In particular, we study the simple connectedness of such components. We also bring up the definitions of Speiser class $\cS$ and Eremenko–Lyubich class $\cB$ and we prove some structural theorems about their Fatou components. In particular, we prove no existence of Baker domains and wandering domains (Sullivan Nonwandering Theorem) for class $\cS$, the latter in Appendix B.