Cyclic Renormalization and Automorphism Groups of Rooted Trees
Bass, Hyman.
Cyclic Renormalization and Automorphism Groups of Rooted Trees [electronic resource] / by Hyman Bass, Maria Victoria Otero-Espinar, Daniel Rockmore, Charles Tresser. - XXII, 174 p. online resource. - Lecture Notes in Mathematics, 1621 0075-8434 ; . - Lecture Notes in Mathematics, 1621 .
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.
9783540478126
10.1007/BFb0096321 doi
Group theory.
Cell aggregation--Mathematics.
Global analysis (Mathematics).
Group Theory and Generalizations.
Manifolds and Cell Complexes (incl. Diff.Topology).
Analysis.
QA174-183
512.2
Cyclic Renormalization and Automorphism Groups of Rooted Trees [electronic resource] / by Hyman Bass, Maria Victoria Otero-Espinar, Daniel Rockmore, Charles Tresser. - XXII, 174 p. online resource. - Lecture Notes in Mathematics, 1621 0075-8434 ; . - Lecture Notes in Mathematics, 1621 .
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.
9783540478126
10.1007/BFb0096321 doi
Group theory.
Cell aggregation--Mathematics.
Global analysis (Mathematics).
Group Theory and Generalizations.
Manifolds and Cell Complexes (incl. Diff.Topology).
Analysis.
QA174-183
512.2