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From the Publisher"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 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.
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.
Posted March 22, 2005
The geometry and dynamics of limit sets is one of the more exciting new trends in mathematics; a subject at the interface of analysis and discrete mathematics. The book is addressed to the beginning graduate level, but it will likely be useful to anyone who wishes to get a feeling for this active and new mathematical area. The examples include conformal measures, iteration of polynomial like mappings, Kleinian groups, multifractal analysis. The main topics are (by chapter) symbolic dynamics, families of functions and their conformal measures, graph and Markov systems, iterated function systems, and topics in dynamics, e.g., rigidity, parabolic systems, Hausdorff and packing measures.) Each subject is attractively presented and followed up to the level of current research. The presentation is clear and concise, and the book can be used in the class room, or for self study. The topics progress logically, and the book represents a coherent unity of ideas, but it can also be used by anyone who wishes to learn just one part of the material, for example conformal iterated function systems. Reviewed by Palle Jorgensen, March 2005.Was this review helpful? Yes NoThank you for your feedback. Report this reviewThank you, this review has been flagged.