Conformal Fractals

Ergodic Theory Methods
Erscheinungsjahr 2011
ISBN: 978-0-521-43800-1
Verlag: Cambridge University Press

Buch, Englisch, Band 371, 364 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 594 g

Reihe: London Mathematical Society Lecture Note Series

• A self-contained introduction suitable for graduate students, including exercises
• Brings together a wide variety of methods and results previously scattered throughout the literature
• Provides pointers to further reading and links to related areas of research
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.

Autoren/Hrsg.

Przytycki, Feliks

Urbanski, Mariusz

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

Introduction
Basic examples and definitions
1. Measure preserving endomorphisms
2. Compact metric spaces
3. Distance expanding maps
4. Thermodynamical formalism
5. Expanding repellers in manifolds and in the Riemann sphere, preliminaries
6. Cantor repellers in the line, Sullivan's scaling function, application in Feigenbaum universality
7. Fractal dimensions
8. Conformal expanding repellers
9. Sullivan's classification of conformal expanding repellers
10. Holomorphic maps with invariant probability measures of positive Lyapunov exponent
11. Conformal measures
References
Index.

Über Autor(innen)

Urbanski, Mariusz
Mariusz Urbanski is a Professor in the Department of Mathematics at the University of North Texas.

Przytycki, Feliks
Feliks Przytycki is a Professor in the Institute of Mathematics at the Polish Academy of Sciences.