Overview

"The theme of this 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 automorhpism groups of such ""spherically homogenous"" rooted trees is investigated in detail. This work should be of interest to researchers in both dynamical systems and group theory."

Full Product Details

Author:   Hyman Bass ,  Maria V. Otero-Espinar ,  Daniel Rockmore ,  Charles Tresser
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   1996 ed.
Volume:   1621
Dimensions:   Width: 15.50cm , Height: 1.00cm , Length: 23.50cm
Weight:   0.630kg
ISBN:  

9783540605959

ISBN 10:   3540605959
Pages:   174
Publication Date:   14 December 1995
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Cyclic renormalization.- Itinerary calculus and renormalization.- Spherically transitive automorphisms of rooted trees.- Closed normal subgroups of Aut(X(q)).

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