Self-Similar Groups - Volodymyr Nekrashevych

Self-Similar Groups

Buch | Softcover
231 Seiten
2005
American Mathematical Society (Verlag)
978-1-4704-7691-5 (ISBN)
147,95 inkl. MwSt
Self-similar groups (groups generated by automata) appeared initially as examples of groups that are easy to define but that enjoy exotic properties like nontrivial torsion, intermediate growth, etc.

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.

Volodymyr Nekrashevych, International University Bremen, Germany, and Kyiv Taras Shevchenko University, Ukraine.

Chapters
1. Basic definitions and examples
2. Algebraic theory
3. Limit spaces
4. Orbispaces
5. Iterated monodromy groups
6. Examples and applications

Erscheint lt. Verlag 31.1.2005
Reihe/Serie Mathematical Surveys and Monographs ; 117
Verlagsort Providence
Sprache englisch
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Geometrie / Topologie
ISBN-10 1-4704-7691-6 / 1470476916
ISBN-13 978-1-4704-7691-5 / 9781470476915
Zustand Neuware
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