Meromorphic Dynamics: Volume 2

Elliptic Functions with an Introduction to the Dynamics of Meromorphic Functions
Erscheinungsjahr 2023
ISBN: 978-1-009-21597-8
Verlag: Cambridge University Press

Buch, Englisch, 480 Seiten, Format (B × H): 152 mm x 232 mm, Gewicht: 907 g

Reihe: New Mathematical Monographs

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.

Autoren/Hrsg.

Kotus, Janina

Urba&

Urbanski, Mariusz

Fachgebiete

• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Technische Thermodynamik
• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen
• Mathematik | Informatik Mathematik Topologie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Inhaltsverzeichnis

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.

Über Autor(innen)

Urbanski, Mariusz
Mariusz Urbanski is Professor of Mathematics at the University of North Texas. His research interests include dynamical systems, ergodic theory, fractal geometry, iteration of rational and meromorphic functions, open dynamical systems, iterated function systems, Kleinian groups, diophantine approximations, topology and thermodynamic formalism. He is the author of eight books, seven monographs, and more than 200 papers.

Kotus, Janina
Janina Kotus is Professor of Mathematics at the Warsaw University of Technology, Poland. Her research focuses on dynamical systems, in particular holomorphic dynamical systems. Together with I. N. Baker and Y. Lu she laid the foundations for iteration of meromophic functions.