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
15 - Rationally Indifferent Periodic Points
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
In this chapter, we provide a very detailed qualitative and quantitative description of the local behavior of iterates of locally and globally defined analytic functions around their rationally indifferent periodic points. We also examine the structure of corresponding Leau–Fatou flower petals, including the Fatou Flower Petal Theorem. These will be frequently used in further chapters of the book devoted to the study of compactly nonrecurrent parabolic elliptic functions.
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- Meromorphic DynamicsElliptic Functions with an Introduction to the Dynamics of Meromorphic Functions, pp. 85 - 122Publisher: Cambridge University PressPrint publication year: 2023