Cyclic Renormalization and Automorphism Groups of Rooted Trees

1996
ISBN: 978-3-540-60595-9
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1621, 174 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 306 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Bass, Hyman

Tresser, Charles

Otero-Espinar, Maria V.

Rockmore, Daniel

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme

Inhaltsverzeichnis

Cyclic renormalization.- Itinerary calculus and renormalization.- Spherically transitive automorphisms of rooted trees.- Closed normal subgroups of Aut(X(q)).