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  • Book
  • © 1996

Cyclic Renormalization and Automorphism Groups of Rooted Trees

Authors:

  1. Hyman Bass
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  2. Maria Victoria Otero-Espinar
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  3. Daniel Rockmore
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  4. Charles Tresser
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1621)

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Table of contents (4 chapters)

  1. Front Matter

    Pages I-XXI
    PDF

  2. Cyclic renormalization

    • Hyman Bass, Maria Victoria Otero-Espinar, Daniel Rockmore, Charles Tresser
    Pages 1-51

  3. Itinerary calculus and renormalization

    • Hyman Bass, Maria Victoria Otero-Espinar, Daniel Rockmore, Charles Tresser
    Pages 53-101

  4. Spherically transitive automorphisms of rooted trees

    • Hyman Bass, Maria Victoria Otero-Espinar, Daniel Rockmore, Charles Tresser
    Pages 103-133

  5. Closed normal subgroups of Aut(X(q))

    • Hyman Bass, Maria Victoria Otero-Espinar, Daniel Rockmore, Charles Tresser
    Pages 135-156

  6. Back Matter

    Pages 157-163
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About this book

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.
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Keywords

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Bibliographic Information

  • Book Title: Cyclic Renormalization and Automorphism Groups of Rooted Trees

  • Authors: Hyman Bass, Maria Victoria Otero-Espinar, Daniel Rockmore, Charles Tresser

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0096321

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1996

  • Softcover ISBN: 978-3-540-60595-9Published: 14 December 1995

  • eBook ISBN: 978-3-540-47812-6Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XXII, 174

  • Topics: Group Theory and Generalizations, Manifolds and Cell Complexes (incl. Diff.Topology), Analysis

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Buy it now

eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

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