Graph directed Markov systems : geometry and dynamics of limit sets / R. Daniel Mauldin and Mariusz Urbaʹnski.

Format:

Book

Author/Creator:

Mauldin, R. Daniel, 1943- author.

Urbański, Mariusz, author.

Series:

Cambridge tracts in mathematics ; 148.

Cambridge tracts in mathematics ; 148

Language:

English

Subjects (All):

Markov processes.

Graph theory.

Geometric function theory.

Limit theorems (Probability theory).

Physical Description:

1 online resource (xi, 281 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2003.

Language Note:

English

Summary:

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.

Contents:

Introduction

1. Preliminaries

2. Symbolic dynamics

3. Hl̲der 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.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 272-279) and index.

ISBN:

1-107-13767-5

1-280-43106-7

9786610431069

0-511-20436-1

0-511-06245-1

0-511-18025-X

0-511-30722-5

0-511-54305-0

0-511-07091-8

OCLC:

770008750