Graph Directed Markov Systems
Geometry and Dynamics of Limit Sets
1st Edition
Published on 20. December 2004
978-0-511-05612-3 (ISBN)
Description
The main focus of this book is the exploration of the geometric and dynamic properties of a far reaching generalization of a conformal iterated function system - a Graph Directed Markov System. These systems are very robust in that they apply to many settings that do not fit into the scheme of conformal iterated systems. The basic theory is laid out here and the authors have touched on many natural questions arising in its context. However, they also emphasise the many issues and current research topics which can be found in original papers. For example the detailed analysis of the structure of harmonic measures of limit sets, the examination of the doubling property of conformal measures, the extensive study of generalized polynomial like mapping or multifractal analysis of geometrically finite Kleinian groups. This book leads readers onto frontier research in the field, making it ideal for both established researchers and graduate students.
Reviews / Votes
"The authors provide in this monograph a state-of-the-art account on the geometry and dynamics of limit sets arising from graph directed Markov systems (GDMS)."Marc Kessebohmer, Mathematical Reviews
More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises
File size
2,79 MB
ISBN-13
978-0-511-05612-3 (9780511056123)
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Schweitzer Classification
Other editions
Additional editions
R. Daniel Mauldin | Mariusz Urbanski
Graph Directed Markov Systems
Geometry and Dynamics of Limit Sets
Book
08/2003
Cambridge University Press
€154.10
Shipment within 15-20 days
Persons
Content
Introduction; 1. Symbolic dynamics; 3. Hoelder families of functions; 4. Conformal graph directed Markov systems; 5. Examples of graph directed Markov systems; 6. Conformal iterated function systems; 7. Dynamical rigidity of conformal iterated function systems; 8. Parabolic iterated function systems; 9. Parabolic systems: Hausdorff and packing measures.
