Geometry of $Q$-recurrent maps
Dynamical Systems
2007-05-23 v1
Abstract
Given a critically periodic quadratic map with no secondary renormalizations, we introduce the notion of -recurrent quadratic polynomials. We show that the pieces of the principal nest of a -recurrent map converge in shape to the Julia set of . We use this fact to compute analytic invariants of the nest of , to give a complete characterization of complex quadratic Fibonacci maps and to obtain a new auto-similarity result on the Mandelbrot set.
Cite
@article{arxiv.math/0311359,
title = {Geometry of $Q$-recurrent maps},
author = {Rodrigo A. Pérez},
journal= {arXiv preprint arXiv:math/0311359},
year = {2007}
}
Comments
8 figures