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Cyclic Renormalization and Automorphism Groups of Rooted Trees (Paperback, 1996 ed.)
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Cyclic Renormalization and Automorphism Groups of Rooted Trees (Paperback, 1996 ed.)
Series: Lecture Notes in Mathematics, 1621
Expected to ship within 10 - 15 working days
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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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