Conformal Fractals

This book serves as an essential guide to ergodic theory and holomorphic iteration, perfect for graduate students and researchers alike.

In Conformal Fractals, readers are introduced to the fascinating intersection of ergodic theory and holomorphic iteration. The authors, drawing from their extensive teaching experience, present a comprehensive overview of the essential tools from ergodic theory and thermodynamic formalism. This foundational knowledge is crucial for understanding the recent advancements in the study of one-dimensional holomorphic iterations and the associated fractal sets, all viewed through the lens of geometric measure theory and rigidity.

The book is structured to cater to both graduate students and researchers, making it a valuable resource for anyone venturing into this rapidly evolving field. It begins with introductory chapters that lay the groundwork, followed by detailed discussions on recent developments. The authors have included thorough proofs to ensure that readers can follow the derivations and concepts clearly. This careful approach not only aids in comprehension but also encourages readers to engage with the material more deeply.

Moreover, Conformal Fractals is designed to facilitate independent research, providing a springboard for further exploration. Helpful exercises are interspersed throughout the text, reinforcing the concepts presented and enhancing the reader's understanding. Additionally, the authors offer links to further reading, ensuring that readers can easily access related areas of research, making this book an essential addition to any academic library.