Self-similar groups

by Nekrashevych, Volodymyr

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Title Statements

Full title :Self-similar groups / Volodymyr Nekrashevych.

Summary

"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."--Jacket.

Edition Statements

Publication Date:©2005.

Publication Statements

Publisher(s):American mathematical Society
Place of Publication:Providence, RI
Language:eng
Publication Date:©2005.

The Physical Object

Description:xi, 231 pages : : illustrations ; : 26 cm.

Edition Identifiers

ISBN:0821838318, 9780821838310
oclc:ocm60321607
LC Classification:QA183
Dewey Decimal:512/.2

Subjects

31.21 theory of groups Dynamique symbolique Geometric group theory Gruppe Gruppe (Mathematik) Gruppentheorie Processus autosimilaires Selbstähnlichkeit Self-similar processes Symbolic dynamics Teoria geométrica dos grupos Théorie géométrique des groupes