Cyclic Renormalization and Automorphism Groups of Rooted Trees

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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.

Book details

Edition:
1996
Series:
Lecture Notes in Mathematics (Book 1621)
Author:
Hyman Bass, Maria V. Otero-Espinar, Daniel Rockmore, Charles Tresser
ISBN:
9783540478126
Related ISBNs:
9783540605959
Publisher:
Springer Berlin Heidelberg
Pages:
N/A
Reading age:
Not specified
Includes images:
No
Date of addition:
2022-08-07
Usage restrictions:
Copyright
Copyright date:
1996
Copyright by:
N/A 
Adult content:
No
Language:
English
Categories:
Mathematics and Statistics, Nonfiction