Mathematical Surveys and Monographs 2005; 231 pp; hardcover Volume: 117 ISBN10: 0821838318 ISBN13: 9780821838310 List Price: US$69 Member Price: US$55.20 Order Code: SURV/117
 Selfsimilar groups (groups generated by automata) initially appeared as examples of groups that are easy to define but have exotic properties like nontrivial torsion, intermediate growth, etc. This book studies the selfsimilarity phenomenon in group theory and shows its intimate relationship with dynamical systems and more classical selfsimilar structures, such as fractals, Julia sets, and selfaffine tilings. This connection is established through the central topics of the book, which are the notions of the iterated monodromy group and limit space. A wide variety of examples and different applications of selfsimilar groups to dynamical systems and vice versa are discussed. In particular, it is shown that Julia sets can be reconstructed from the respective iterated monodromy groups and that groups with exotic properties can appear not just as isolated examples, but as naturally defined iterated monodromy groups of rational functions. The book offers important, new mathematics that will open new avenues of research in group theory and dynamical systems. It is intended to be accessible to a wide readership of professional mathematicians. Readership Graduate students and research mathematicians interested in group theory and dynamical systems. Table of Contents  Basic definitions and examples
 Algebraic theory
 Limit spaces
 Orbispaces
 Iterated monodromy groups
 Examples and applications
 Bibliography
 Index
