Graph Directed Markov Systems
Geometry and Dynamics of Limit Sets

Monograph on Graph Directed Markov Systems with backgound and research level material.

R. Daniel Mauldin (Author), Mariusz Urbanski (Author)

9780521825382, Cambridge University Press

Hardback, published 7 August 2003

294 pages
23.5 x 16.1 x 2.3 cm, 0.541 kg

"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

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.

Introduction
1. Symbolic dynamics
3. Hölder 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.

Subject Areas: Nonlinear science [PBWR], Calculus & mathematical analysis [PBK]