Cyclic renormalization and automorphism groups of rooted trees
By: Hyman Bass ... [et al.].
Contributors: Bass, Hyman, 1932-
Series: Lecture notes in mathematics ;; 1621; Lecture notes in mathematics (Springer-Verlag) ;; 1621.
Publisher: Springer-Verlag
Published: 1996
Place of publication: Berlin; New York
Language: eng
Number of pages: 163
Subjects: Differentiable dynamical systems; Group theory; Automorphisms
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.
Notes: Includes bibliographical references (p. [157]-159) and index.