Graph Directed Markov Systems: Geometry and Dynamics of Limit Sets (Cambridge Tracts in Mathematics) [Hardcover]

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

Book Description

ISBN-10: 0521825385 | ISBN-13: 978-0521825382 | Publication Date: August 18, 2003

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.

Editorial Reviews

Review

"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

Book Description

The main focus of this book is the development of the theory of Graph Directed Markov Systems. This far reaching generalisation of the theory of conformal iterated systems can be applied in many situations, including the theory of dynamical systems. This text is very timely and is written by acknowledged experts in the field. The authors have included much of the necessary background material to increase the appeal of this book to graduate students as well as researchers. There is also an extensive list of references suggesting further reading.

Product Details

• Hardcover: 294 pages
• Publisher: Cambridge University Press (August 18, 2003)
• Language: English
• ISBN-10: 0521825385
• ISBN-13: 978-0521825382
• Product Dimensions: 9.2 x 5.8 x 0.8 inches
• Shipping Weight: 1.1 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #3,954,458 in Books (See Top 100 in Books)

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2 of 2 people found the following review helpful:

5.0 out of 5 stars A nice entry into a new trend in dynamics and limit sets., March 22, 2005

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Palle E T Jorgensen "Palle Jorgensen" (Iowa City, Iowa United States) - See all my reviews
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This review is from: Graph Directed Markov Systems: Geometry and Dynamics of Limit Sets (Cambridge Tracts in Mathematics) (Hardcover)

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.