Self-similar Groups

Self-similar Groups
ISBN-10
0821838318
ISBN-13
9780821838310
Category
Geometric group theory
Pages
231
Language
English
Published
2005
Publisher
American Mathematical Soc.
Author
Volodymyr Nekrashevych

Description

The book studies the self-similarity phenomenon in group theory and shows its intimate relation with dynamical systems and more classical self-similar structures, such as fractals, Julia sets, and self-affine tilings. The relation is established through the notions of the iterated monodromy group and the limit space, which are the central topics of the book. A wide variety of examples and different applications of self-similar groups to dynamical systems and vice versa are discussed. It is shown in particular how Julia sets can be reconstructed from the respective iterated monodromy groups and that groups with exotic properties appear now not just as isolated examples but as naturally defined iterated monodromy groups of rational functions. The book is intended to be accessible, to a wide mathematical readership, including graduate students interested in group theory and dynamical systems.

Get the book

Amazon.com
Amazon.com
Search the book
eBay.com
eBay.com
Search the book

Similar books

  • Axes in Outer Space
    Axes in Outer Space
    By Michael Handel, Lee Mosher

    (3) If f, (3) = b and d is a direction based at a then • For some m > 0, j"(a) e Fix(g). • f,(g"(a)) and Df,(Dg" (d)) are independent of k > 0. (4) The assignment (p → b = Fix(pl.) of (1) defines a bijection between PA(Q) and the set ...

  • Irreducible Geometric Subgroups of Classical Algebraic Groups
    Irreducible Geometric Subgroups of Classical Algebraic Groups
    By , Timothy C. Burness, Soumaia Ghandour

    Timothy C. Burness,, Soumaïa Ghandour, Donna M. Testerman. Rough description C1 Stabilizers ... The Ci collections that the Jordan normal form of x on W comprises an even number of unipotent Jordan blocks of size 2 (see [2, Section 8]).

  • Geometric Group Theory
    Geometric Group Theory
    By Michael Kapovich, Cornelia Druţu

    T. Ceccherini-Silberstein, R. Grigorchuk, and P. de la Harpe, Décompositions paradoxales des groupes de Burnside, C. R. Acad. Sci. Paris Sér. I Math. 327 (1998), no. 2, 127–132. N. J. Cutland, Loeb measures in practice: Recent advances, ...

  • Geometric and Cohomological Methods in Group Theory
    By Martin R. Bridson, Peter H. Kropholler, Ian J. Leary

    An extended tour through a selection of the most important trends in modern geometric group theory.

  • Quasi-Actions on Trees II: Finite Depth Bass-Serre Trees
    Quasi-Actions on Trees II: Finite Depth Bass-Serre Trees
    By Michah Sageev, Lee Mosher, Kevin Whyte

    ... 2011 Palle E. T. Jorgensen, Keri A. Kornelson, and Karen L. Shuman, Iterated function systems, moments, and transformations of infinite matrices, 2011 Man Chun Leung, Supported blow-up and prescribed scalar curvature on Sn, ...