Cyclic Renormalization and Automorphism Groups of Rooted Trees par Hyman Bass

Cyclic Renormalization and Automorphism Groups of Rooted Trees par Hyman Bass

Titre de livre: Cyclic Renormalization and Automorphism Groups of Rooted Trees

Auteur: Hyman Bass

Broché: 174 pages

Date de sortie: December 14, 1995

ISBN: 3540605959

Éditeur: Springer

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Hyman Bass avec Cyclic Renormalization and Automorphism Groups of Rooted Trees

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.