Cyclic Renormalization and Automorphism Groups of Rooted Trees

  • Authors
  • Hyman Bass
  • Maria Victoria Otero-Espinar
  • Daniel Rockmore
  • Charles Tresser
Book
Part of the Lecture Notes in Mathematics book series (LNM, volume 1621)

Table of contents

  1. Front Matter
    Pages I-XXI
  2. Hyman Bass, Maria Victoria Otero-Espinar, Daniel Rockmore, Charles Tresser
    Pages 1-51
  3. Hyman Bass, Maria Victoria Otero-Espinar, Daniel Rockmore, Charles Tresser
    Pages 53-101
  4. Hyman Bass, Maria Victoria Otero-Espinar, Daniel Rockmore, Charles Tresser
    Pages 103-133
  5. Hyman Bass, Maria Victoria Otero-Espinar, Daniel Rockmore, Charles Tresser
    Pages 135-156
  6. Back Matter
    Pages 157-163

About this book

Introduction

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.

Keywords

Group theory automorphism calculus dynamical systems

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0096321
  • Copyright Information Springer-Verlag Berlin Heidelberg 1996
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-60595-9
  • Online ISBN 978-3-540-47812-6
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book