The complex a priori bounds for bounded primitive renormalization
Date and Time:
Wednesday, March 8, 2006 - 11:45am to 12:35pm
Location:
Fields Institute, Room 230
Abstract:
Let f(z) = z2 +c be infinitely renormalizable of bounded primitive type; it admits an infinite sequence of primitive renormalizations, and the period of each is a bounded multiple of the next-smaller period. We show by means of a combinatorial approximation of the geometry that ”if it is bad now, it was worse earlier”: if some primitive renormalization can be performed only with small modulus, then there is a previous level that can be performed only with smaller modulus. It follows immediately that all renormalizations can be performed with modulus bounded below.