Meromorphic Dynamics: Volume 1
Abstract Ergodic Theory, Geometry, Graph Directed Markov Systems, and Conformal Measures

A comprehensive and detailed presentation of finite and infinite ergodic theory, fractal measures, and thermodynamic formalism.

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

9781009215916, Cambridge University Press

Hardback, published 4 May 2023

420 pages
23.5 x 15.6 x 3.1 cm, 0.85 kg

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.

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.

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]