Conformal Fractals: Ergodic Theory Methods (London Mathematical Society Lecture Note Series, Series Number 371) 1st Edition by Feliks Przytycki (PDF)

Description

This is a one-stop introduction to the methods of ergodic theory applied to holomorphic iteration. The authors begin with introductory chapters presenting the necessary tools from ergodic theory thermodynamical formalism, and then focus on recent developments in the field of 1-dimensional holomorphic iterations and underlying fractal sets, from the point of view of geometric measure theory and rigidity. Detailed proofs are included. Developed from university courses taught by the authors, this book is ideal for graduate students. Researchers will also find it a valuable source of reference to a large and rapidly expanding field. It eases the reader into the subject and provides a vital springboard for those beginning their own research. Many helpful exercises are also included to aid understanding of the material presented and the authors provide links to further reading and related areas of research.

User’s Reviews

Editorial Reviews: Review “This book provides a broad and self-contained introduction to the theory of uniformly and non-uniformly expanding holomorphic maps. This book is a valuable resource for fundamental results and a comprehensive state of the art reference for recent developments in the field.” Katrin Gelfert, Mathematical Reviews”Conformal Fractals is packed with classical gems with proofs provided. The authors are experts on extending the subject in many of the important directions it has taken the past several decades, especially the move from uniformly hyperbolic maps to expansive maps, which includes many rational maps of the sphere. This is an interesting text that could be used for a year-long graduate course in ergodic theory…” Jane Hawkins, Bulletin of the American Mathematical Society Book Description A one-stop introduction to the methods of ergodic theory applied to holomorphic iteration that is ideal for graduate courses. About the Author Feliks Przytycki is a Professor in the Institute of Mathematics at the Polish Academy of Sciences.Mariusz Urbanski is a Professor in the Department of Mathematics at the University of North Texas. Read more

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