Meromorphic Dynamics: Volume 1

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

This text, the first of two volumes, provides a comprehensive and self-contained approach to many fundamental results from ergodic theory and geometric measure theory. All key concepts are carefully explained and full proofs are provided in this indispensable reference for any researchers interested in low-dimensional dynamics.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.