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Viser: Meromorphic Dynamics: Volume 2 - Elliptic Functions with an Introduction to the Dynamics of Meromorphic Functions
Meromorphic Dynamics: Volume 2
Elliptic Functions with an Introduction to the Dynamics of Meromorphic Functions
Janina Kotus og Mariusz UrbaÅ?ski
(2023)
Sprog: Engelsk
Cambridge University Press
1.861,00 kr.
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Detaljer om varen
- Hardback: 480 sider
- Udgiver: Cambridge University Press (Maj 2023)
- Forfattere: Janina Kotus og Mariusz UrbaÅ?ski
- ISBN: 9781009215978
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.
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.
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