Meromorphic Dynamics: Volume 2

ISBN-13: 9781009215978 / Twarda / 2023

Mariusz (University of North Texas) Urbanski

Opis

The first monograph to explore the beautiful and rich dynamics of elliptic functions, with an emphasis on ergodic aspects.

Spis treści

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.