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

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.