Graph Directed Markov Systems: Geometry and Dynamics of Limit Sets by R. Daniel Mauldin, Mariusz Urbanski, W. Fulton (Contribution by), B. Simon (Contribution by), A. Katok (Contribution by)

Graph Directed Markov Systems: Geometry and Dynamics of Limit Setsby Anonymous

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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.