Graph directed Markov systems : Geometry and dynamics of limit sets

R. Daniel Mauldin, Mariusz Urbanski

292 pages, parution le 28/07/2003

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Résumé

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

Preliminaries
Symbolic dynamics
Hölder families of functions and F-conformal measures
Conformal graph directed Markov systems
Examples of GDMSs
Conformal iterated function systems
Dynamical rigidity of CIFSs
Parabolic iterated function systems
Parabolic systems: Hausdorff and packing measures

Appendixes
Glossary of notation
Bibliography
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	R. Daniel Mauldin, Mariusz Urbanski
Parution	28/07/2003
Nb. de pages	292
Format	15,7 x 23,5
Couverture	Relié
Poids	535g
Intérieur	Noir et Blanc
EAN13	9780521825382
ISBN13	978-0-521-82538-2