Geometry of $Q$-recurrent maps
Abstract
Description
Given a critically periodic quadratic map with no secondary
renormalizations, we introduce the notion of $Q$-recurrent quadratic
polynomials. We show that the pieces of the principal nest of a
$Q$-recurrent map $f_c$ converge in shape to the Julia set of $Q$. We use
this fact to compute analytic invariants of the nest of $f_c$, to give a
complete characterization of complex quadratic Fibonacci maps and to obtain
a new auto-similarity result on the Mandelbrot set.
8 figures
8 figures