Cyclic Renormalization and Automorphism Groups of Rooted Trees
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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.
Format:Paperback
Language:English
ISBN:3540605959
ISBN13:9783540605959
Release Date:December 1995
Publisher:Springer
Length:174 Pages
Weight:0.62 lbs.
Dimensions:0.4" x 6.1" x 9.2"
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