Graph Directed Markov Systems: Geometry and Dynamics of Limit Sets

by R. Daniel Mauldin, Mariusz Urbanski

Overview

The main focus of this book is on the development of the theory of Graph Directed Markov Systems. This far-reaching generalization of the theory of conformal iterated systems can be applied in many situations, including the theory of dynamical systems. Dan Mauldin and Mariusz Urbanski include much of the necessary background material to increase the appeal of this book to graduate students as well as researchers. They also include an extensive list of references for further reading.

Product Details

ISBN-13:	9780521825382
Publisher:	Cambridge University Press
Publication date:	08/07/2003
Series:	Cambridge Tracts in Mathematics , #148
Pages:	294
Product dimensions:	6.34(w) x 9.25(h) x 0.91(d)

Table of Contents

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.

Editorial Reviews

"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

From the Publisher