Meromorphic Dynamics
Meromorphic Dynamics
CAD$195.95
This text, the second of two volumes, builds on the foundational material on ergodic theory and geometric measure theory provided in Volume I, and applies all the techniques discussed to describe the beautiful and rich dynamics of elliptic functions. The text begins with an introduction to topological dynamics of transcendental meromorphic functions, before progressing to elliptic functions, discussing at length their classical properties, measurable dynamics and fractal geometry. The authors then look in depth at compactly non-recurrent elliptic functions. Much of this material is appearing for the first time in book or paper form. Both senior and junior researchers working in ergodic theory and dynamical systems will appreciate what is sure to be an indispensable reference.
- Largely self-contained, with detailed proofs
- Highlights the connections between various subfields and aspects of dynamical systems ergodic theory, and other areas of mathematics
- Brings together research previously scattered across many different papers, and contains new material not previously published elsewhere
Product details
April 2023Adobe eBook Reader
9781009215961
0 pages
This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
- Volume II. 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:
- 16. Classics of elliptic functions: selected properties
- 17. Geometry and dynamics of (all) elliptic functions
- Part V. Compactly Nonrecurrent Elliptic Functions: First Outlook:
- 18. Dynamics of compactly norecurrent elliptic functions
- 19. Various examples of compactly nonrecurrent elliptic functions
- 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.
