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
978-3-540-60595-9, 978-3-540-47812-6
DOI
10.1007/BFb0096321
Language
english
Format
PDF
Filesize
2 MB (2292486 bytes)
Series
Lecture Notes in Mathematics 1621
Edition
1
Pages
174\178
Orientation
yes
Scanned
yes
Time added
2013-08-01 04:00:00
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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