Graph directed Markov systems
Subtitle: geometry and dynamics of limit sets
By: R. Daniel Mauldin and Mariusz Urbaʹnski.
Contributors: Urbaʹnski, Mariusz.
Series: Cambridge tracts in mathematics ;; 148
Publisher: Cambridge University Press
Published: 2003
Place of publication: Cambridge
Language: eng
Number of pages: 281
Subjects: Markov processes.; Graph theory.; Geometric function theory.; Limit theorems (Probability theory)
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.
Notes: Includes bibliographical references (p. 272-279) and index.