ENGLISH

Cyclic Renormalization and Automorphism Groups of Rooted Trees

By Hyman Bass , Maria Victoria Otero-Espinar , Daniel Rockmore , Charles Tresser (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1996
ISBN
3540605959, 9783540605959
DOI
10.1007/BFb0096321
LCC
QA3 .L28 no. 1621,QA614.8 .L28 no. 1621
Open Library ID
OL809707M
Language
english
Format
DJVU
Filesize
959 kB (982179 bytes)
Series
Lecture Notes in Mathematics 1621
Edition
1
Pages
174\182
Library
Kolxo3
DPI
300
Time added
2009-07-20 03:45:11
Group Theory and Generalizations; Manifolds and Ce

Description

The theme of the monograph is an interplay between dynamical systems and group theory. The authors formalize and study "cyclic renormalization", a phenomenon which appears naturally for some interval dynamical systems. A possibly infinite hierarchy of such renormalizations is naturally represented by a rooted tree, together with a "spherically transitive" automorphism; the infinite case corresponds to maps with an invariant Cantor set, a class of particular interest for its relevance to the description of the transition to chaos and of the Mandelbrot set. The normal subgroup structure of the automorphism group of such "spherically homogeneous" rooted trees is investigated in some detail. This work will be of interest to researchers in both dynamical systems and group theory.

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