Cyclic Renormalization and Automorphism Groups of Rooted Trees. 1st ed. 1996

種類:

電子ブック

責任表示:

by Hyman Bass, Maria V. Otero-Espinar, Daniel Rockmore, Charles Tresser

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1996

著者名:

• Bass, Hyman.
• Otero-Espinar, Maria V.
• Rockmore, Daniel.
• Tresser, Charles.
• SpringerLink (Online service)

シリーズ名:

Lecture Notes in Mathematics ; 1621

ISBN:

9783540478126 [3540478124]    

注記:

Cyclic renormalization -- Itinerary calculus and renormalization -- Spherically transitive automorphisms of rooted trees -- Closed normal subgroups of Aut(X(q)).
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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