
Table of Contents 
Fields Institute Communications 2008; 395 pp; hardcover Volume: 53 ISBN10: 0821842757 ISBN13: 9780821842751 List Price: US$130 Member Price: US$104 Order Code: FIC/53 See also: Universality and Renormalization: From Stochastic Evolution to Renormalization of Quantum Fields  Ilia Binder and Dirk Kreimer Fractal Geometry and Applications: A Jubilee of Benoît Mandelbrot  Michel L Lapidus and Machiel van Frankenhuijsen  The papers collected in this volume reflect some of the directions of research in two closely related fields: Complex Dynamics and Renormalization in Dynamical Systems. While dynamics of polynomial mappings, particularly quadratics, has by now reached a mature state of development, much less is known about nonpolynomial rational maps. The reader will be introduced into this fascinating world and a related area of transcendental dynamics by the papers in this volume. A graduate student will find an area rich with open problems and beautiful computer simulations. A survey by V. Nekrashevych introduces the reader to iterated monodromy groups of rational mappings, a recently developed subject that links geometric group theory to combinatorics of rational maps. In this new language, many questions related to Thurston's theory of branched coverings of the sphere can be answered explicitly. Renormalization theory occupies a central place in modern Complex Dynamics. The progress in understanding the structure of the Mandelbrot set, polynomial Julia sets, and Feigenbaumtype universalities stems from renormalization techniques. Renormalization of circle maps and rotation domains, such as Siegel disks, can be understood in the context of the classical KAM theory. Corresponding phenomena in higher dimensions, such as universal scaling in areapreserving maps in 2D, on the boundary of KAM, pose a challenging problem. A survey by H. Koch and several other papers in the volume will introduce the reader to this direction of study. Titles in this series are copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada). Readership Graduate students and research mathematicians interested in complex dynamical systems and renormalization in dynamics. 


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