SYMBOLIC DYNAMICS FOR ANGLE-DOUBLING ON THE CIRCLE .2. SYMBOLIC DESCRIPTION OF THE ABSTRACT MANDELBROT SET

Authors
Citation
C. Bandt et K. Keller, SYMBOLIC DYNAMICS FOR ANGLE-DOUBLING ON THE CIRCLE .2. SYMBOLIC DESCRIPTION OF THE ABSTRACT MANDELBROT SET, Nonlinearity, 6(3), 1993, pp. 377-392
Citations number
16
Categorie Soggetti
Mathematics,"Mathematical Method, Physical Science",Mathematics,"Physycs, Mathematical
Journal title
ISSN journal
09517715
Volume
6
Issue
3
Year of publication
1993
Pages
377 - 392
Database
ISI
SICI code
0951-7715(1993)6:3<377:SDFAOT>2.0.ZU;2-Q
Abstract
Under the assumption that the Mandelbrot set is locally connected, its boundary can be considered as a topological factor T/approximately of the circle T, which is called the abstract Mandelbrot set. The struct ure of T/approximately is tightly connected with the angle-doubling ma p on T. We give an abstract description of the equivalence relation ap proximately, discuss results by Thurston and Lavaurs from the viewpoin t of symbolic dynamics and study renormalization in the abstract Mande lbrot set.