Meromorphic Dynamics 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
13 - Fundamental Properties of Meromorphic Dynamical Systems
from Part III - Topological Dynamics of Meromorphic Functions
Published online by Cambridge University Press: 20 April 2023
- 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
In this chapter, we provide a relatively short and condensed account of the topological dynamics of all meromorphic functions with an emphasis on Fatou domains, including Baker domains that are exclusive for transcendental functions and do not occur for rational functions. We also carry out a thorough analysis of the singular set of the inverse of a meromorphic function and all its iterates. In particular, we study at length asymptotic values and their relations to transcendental tracts. The results of this analysis will be used very frequently to study the topological structure of connected components (and their boundaries) of Fatou sets in this part of the book and a countless number of times when we move on to dealing with elliptic functions.
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- Meromorphic DynamicsElliptic Functions with an Introduction to the Dynamics of Meromorphic Functions, pp. 3 - 66Publisher: Cambridge University PressPrint publication year: 2023