Meromorphic Dynamics Elliptic Functions with an Introduction to the Dynamics of Meromorphic Functions
Book contents
- Frontmatter
- Dedication
- Contents
- Contents of Volume I
- Preface
- Acknowledgments
- Introduction
- Part III Topological Dynamics of Meromorphic Functions
- 13 Fundamental Properties of Meromorphic Dynamical Systems
- 14 Finer Properties of Fatou Components
- 15 Rationally Indifferent Periodic Points
- Part IV Elliptic Functions: Classics, Geometry, and Dynamics
- Part V Compactly Nonrecurrent Elliptic Functions: First Outlook
- Part VI Compactly Nonrecurrent Elliptic Functions: Fractal Geometry, Stochastic Properties, and Rigidity
- Appendix A A Quick Review of Some Selected Facts from Complex Analysis of a One-Complex Variable
- Appendix B Proof of the Sullivan Nonwandering Theorem for Speiser Class S
- References
- Index of Symbols
- Subject Index
14 - Finer Properties of Fatou Components
from Part III - Topological Dynamics of Meromorphic Functions
Published online by Cambridge University Press: 20 April 2023
Book contents
- Frontmatter
- Dedication
- Contents
- Contents of Volume I
- Preface
- Acknowledgments
- Introduction
- Part III Topological Dynamics of Meromorphic Functions
- 13 Fundamental Properties of Meromorphic Dynamical Systems
- 14 Finer Properties of Fatou Components
- 15 Rationally Indifferent Periodic Points
- Part IV Elliptic Functions: Classics, Geometry, and Dynamics
- Part V Compactly Nonrecurrent Elliptic Functions: First Outlook
- Part VI Compactly Nonrecurrent Elliptic Functions: Fractal Geometry, Stochastic Properties, and Rigidity
- Appendix A A Quick Review of Some Selected Facts from Complex Analysis of a One-Complex Variable
- Appendix B Proof of the Sullivan Nonwandering Theorem for Speiser Class S
- References
- Index of Symbols
- Subject Index
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.
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- Meromorphic DynamicsElliptic Functions with an Introduction to the Dynamics of Meromorphic Functions, pp. 67 - 84Publisher: Cambridge University PressPrint publication year: 2023