Cyclic renormalization and automorphism groups of rooted trees. Lecture notes in mathematics ; Vol. 1621

Bass, Hyman, Maria V. Otero-Espinar Daniel Rockmore u. a.,

ISBN 10: 3540605959 / ISBN 13: 9783540605959

Published by Berlin ; Heidelberg ; Singapore ; Tokyo ; New York ; Barcelona ; Budapest ; Hong Kong ; London ; Milan ; Paris ; Santa Clara : Springer, 1996

About this Item

XXI, 163 pages Ex-Library book in very good condition. 9783540605959 Sprache: Englisch Gewicht in Gramm: 440.

Seller Inventory # 1166240

Bibliographic Details

• Title: Cyclic renormalization and automorphism groups of rooted trees. Lecture notes in mathematics ; Vol. 1621
• Publisher: Berlin ; Heidelberg ; Singapore ; Tokyo ; New York ; Barcelona ; Budapest ; Hong Kong ; London ; Milan ; Paris ; Santa Clara : Springer
• Publication Date: 1996
• Language: English
• ISBN 10: 3540605959
• ISBN 13: 9783540605959
• Binding: kart.
• Seller catalogs:
  • SA MATHEMATIK

About this title

Synopsis

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.