TY  - BOOK
AU  - Bass,Hyman
AU  - Otero-Espinar,Maria Victoria
AU  - Rockmore,Daniel
AU  - Tresser,Charles
ED  - SpringerLink (Online service)
TI  - Cyclic Renormalization and Automorphism Groups of Rooted Trees
T2  - Lecture Notes in Mathematics,
SN  - 9783540478126
AV  - QA174-183 
U1  - 512.2 23
PY  - 1996///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Group theory
KW  - Global analysis (Mathematics)
KW  - Cell aggregation
KW  - Group Theory and Generalizations
KW  - Manifolds and Cell Complexes (incl. Diff.Topology)
KW  - Analysis
N1  - Cyclic renormalization -- Itinerary calculus and renormalization -- Spherically transitive automorphisms of rooted trees -- Closed normal subgroups of Aut(X(q))
N2  - 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
UR  - http://dx.doi.org/10.1007/BFb0096321
ER  -