Cyclic Renormalization and Automorphism Groups of Rooted Trees

Hyman Bass

ISBN 10: 3540605959 / ISBN 13: 9783540605959

Published by Springer, Springer Vieweg, 1995

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9783540605959

Bibliographic Details

• Title: Cyclic Renormalization and Automorphism Groups of Rooted Trees
• Publisher: Springer, Springer Vieweg
• Publication Date: 1995
• Language: English
• ISBN 10: 3540605959
• ISBN 13: 9783540605959
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 11D millimeters 235 millimeters width by 155 millimeters height by 11 millimeters depth
• Weight: 306 grams

About this title

Synopsis

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.