Abstract ergodic theory, geometry, graph directed Markov systems, and conformal measures
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Bibliographic Information
Abstract ergodic theory, geometry, graph directed Markov systems, and conformal measures
（New mathematical monographs, 46 . Meromorphic dynamics ; v. 1）
Cambridge University Press, 2023
1st ed.
Available at / 7 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
KOT||6||1200045056094
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The Institute for Solid State Physics Library. The University of Tokyo.図書室
413.5:M2:17210404245
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Includes bibliographical references (p.469-477) and indexes
Description and Table of Contents
Description
This text, the first of two volumes, provides a comprehensive and self-contained introduction to a wide range of fundamental results from ergodic theory and geometric measure theory. Topics covered include: finite and infinite abstract ergodic theory, Young's towers, measure-theoretic Kolmogorov-Sinai entropy, thermodynamics formalism, geometric function theory, various kinds of conformal measures, conformal graph directed Markov systems and iterated functions systems, semi-local dynamics of analytic functions, and nice sets. Many examples are included, along with detailed explanations of essential concepts and full proofs, in what is sure to be an indispensable reference for both researchers and graduate students.
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.
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