Meromorphic Dynamics: Volume 2
Elliptic Functions with an Introduction to the Dynamics of Meromorphic Functions

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

Janina Kotus (Author), Mariusz Urba?ski (Author)

9781009215978, Cambridge University Press

Hardback, published 4 May 2023

480 pages
23.5 x 15.8 x 3.4 cm, 0.91 kg

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.

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.

Subject Areas: Engineering thermodynamics [TGMB], Topology [PBP], Differential & Riemannian geometry [PBMP], Geometry [PBM], Integral calculus & equations [PBKL], Complex analysis, complex variables [PBKD], Mathematics [PB], Mathematics & science [P]