Meromorphic Dynamics 2 Volume Hardback Set
Meromorphic Dynamics 2 Volume Hardback Set
$260.00
USDThis two-volume set provides a comprehensive and self-contained approach to the dynamics, ergodic theory, and geometry of elliptic functions mapping the complex plane onto the Riemann sphere. Volume I discusses many fundamental results from ergodic theory and geometric measure theory in detail, including finite and infinite abstract ergodic theory, Young's towers, measure-theoretic Kolmogorov-Sinai entropy, thermodynamics formalism, geometric function theory, various conformal measures, conformal graph directed Markov systems and iterated functions systems, classical theory of elliptic functions. In Volume II, all these techniques, along with an introduction to topological dynamics of transcendental meromorphic functions, are applied to describe the beautiful and rich dynamics and fractal geometry of elliptic functions. Much of this material is appearing for the first time in book or even paper form. Both researchers and graduate students will appreciate the detailed explanations of essential concepts and full proofs provided in 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
July 2023Multiple copy pack
9781009216050
400 pages
235 × 157 × 60 mm
1.73kg
Available
Table of Contents
- Volume I. Preface
- Acknowledgments
- Introduction
- Part I. Ergodic Theory and Geometric Measures:
- 1. Geometric measure theory
- 2. Invariant measures: finite and infinite
- 3. Probability (finite) invariant measures: basic properties and existence
- 4. Probability (finite) invariant measures: finer properties
- 5. Infinite invariant measures: finer properties
- 6. measure- theoretic entropy
- 7. Thermodynamic formalism
- Part II. Complex Analysis, Conformal Measures, and Graph Directed Markov Systems:
- 8. Selected topics from complex analysis
- 9. Invariant measures for holomorphic maps f in A(X) or in Aw(X)
- 10. Sullivan conformal measures for holomorphic maps f in A(X) and in Aw(X)
- 11. Graph directed Markov systems
- 12. Nice sets for analytic maps
- References
- Index of symbols
- Subject index
- 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.
