Meromorphic dynamics : Abstract ergodic theory, geometry, graph directed Markov systems, and conformal measures, Vol. 1 - Kotus, Janina; Urbański, Mariusz (Cambridge, United Kingdom ; New York, NY, USA : Cambridge University Press, 2023)
"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 1. abstract ergodic theory, geometry, graph directed Markov systems, and conformal measures -- Volume 2. Elliptic functions with an introduction to the dynamics of meromorphic functions.
Includes bibliographical references and index.
Keywords: Functions, Meromorphic; Ergodic Theory and Geometric Measures; Complex Analysis, Conformal Measures; Graph Directed Markov Systems