| Cyclic Renormalization and Automorphism Groups of Rooted Trees 1996 Edition Contributor(s): Bass, Hyman (Author), Otero-Espinar, Maria V. (Author), Rockmore, Daniel (Author) |
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ISBN: 3540605959 ISBN-13: 9783540605959 Publisher: Springer OUR PRICE: $47.49 Product Type: Paperback Published: December 1995 |
| Additional Information |
| BISAC Categories: - Mathematics | Group Theory - Mathematics | Mathematical Analysis - Mathematics | Topology - General |
| Dewey: 512.2 |
| LCCN: 95046524 |
| Series: Lecture Notes in Physics |
| Physical Information: 0.42" H x 6.14" W x 9.21" (0.62 lbs) 174 pages |
| Descriptions, Reviews, Etc. |
| Publisher 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. |