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
- 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
- 20 Sullivan h-Conformal Measures for Compactly Nonrecurrent Elliptic Functions
- 21 Hausdorff and Packing Measures of Compactly Nonrecurrent Regular Elliptic Functions
- 22 Conformal Invariant Measures for Compactly Nonrecurrent Regular Elliptic Functions
- 23 Dynamical Rigidity of Compactly Nonrecurrent Regular Elliptic Functions
- 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
23 - Dynamical Rigidity of Compactly Nonrecurrent Regular Elliptic Functions
from Part VI - Compactly Nonrecurrent Elliptic Functions: Fractal Geometry, Stochastic Properties, and Rigidity
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
- 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
- 20 Sullivan h-Conformal Measures for Compactly Nonrecurrent Elliptic Functions
- 21 Hausdorff and Packing Measures of Compactly Nonrecurrent Regular Elliptic Functions
- 22 Conformal Invariant Measures for Compactly Nonrecurrent Regular Elliptic Functions
- 23 Dynamical Rigidity of Compactly Nonrecurrent Regular Elliptic Functions
- 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 deal with the dynamical rigidity of compactly nonrecurrent regular elliptic functions. The issue at stake is whether a weak conjugacy such as a Lipschitz one on Julia sets can be promoted to a much better one such as affine on the whole complex plane $\C$. This topic has a long history and goes back at least to the seminal paper by Sullivan, treating among others the dynamical rigidity of conformal expanding repellers. Our approach in this chapter stems from this article by Sullivan.
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- Meromorphic DynamicsElliptic Functions with an Introduction to the Dynamics of Meromorphic Functions, pp. 458 - 488Publisher: Cambridge University PressPrint publication year: 2023