Lecture Notes in Mathematics

2 primary works

Algebraic K-Theory II. Proceedings of the Conference Held at the Seattle Research Center of Battelle Memorial Institute, August 28 - September 8, 1972

by Hyman Bass

Published 1 February 1986

Cyclic Renormalization and Automorphism Groups of Rooted Trees

by Hyman Bass, Maria V. Otero-Espinar, Daniel Rockmore, and Charles Tresser

Published 14 December 1995

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.