Conformal Fractals

Ergodic Theory Methods

Feliks Przytycki, Mariusz Urbański (University of North Texas)

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English

Cambridge University Press
06 May 2010

Calculus & mathematical analysis; Differential calculus & equations; Fractal geometry; Probability & statistics

Series: London Mathematical Society Lecture Note Series

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.

By: Feliks Przytycki, Mariusz Urbański (University of North Texas)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 371
Dimensions: Height: 228mm, Width: 152mm, Spine: 18mm
Weight: 520g
ISBN: 9780521438001
ISBN 10: 0521438004
Series: London Mathematical Society Lecture Note Series
Pages: 366
Publication Date: 06 May 2010
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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.

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.

Reviews for Conformal Fractals: Ergodic Theory Methods

'This is an interesting and substantial book which makes a valuable contribution to the theory of iterations of expanding and non-uniformly expanding holomorphic maps, an area with a long tradition as well as a lot of current activities ... An extensive bibliography and a useful index complete this essential reference in ergodic theory for conformal fractals.' Zentralblatt MATH