Self-Similar Groups

Volume 117

Volodymyr Nekrashevych - Collection Mathematical Surveys and Monographs

234 pages, parution le 22/09/2005

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Résumé

Self-similar 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 self-similarity phenomenon in group theory and shows its intimate relationship with dynamical systems and more classical self-similar structures, such as fractals, Julia sets, and self-affine 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 self-similar 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.

L'auteur - Volodymyr Nekrashevych

Volodymyr Nekrashevych, International University Bremen, and Kyiv Taras Shevchenko University

Sommaire

Basic definitions and examples
Algebraic theory
Limit spaces
Orbispaces
Iterated monodromy groups
Examples and applications
Bibliography

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Caractéristiques techniques

	PAPIER
Éditeur(s)	American Mathematical Society (AMS)
Auteur(s)	Volodymyr Nekrashevych
Collection	Mathematical Surveys and Monographs
Parution	22/09/2005
Nb. de pages	234
Format	18,5 x 26
Couverture	Relié
Poids	660g
Intérieur	Noir et Blanc
EAN13	9780821838310
ISBN13	978-0-8218-3831-0