Quadratic polynomials, multipliers and equidistribution
Dynamical Systems
2013-06-13 v1 Complex Variables
Abstract
Given a sequence of complex numbers {\rho}_n, we study the asymptotic distribution of the sets of parameters c {\epsilon} C such that the quadratic maps z^2 +c has a cycle of period n and multiplier {\rho}_n. Assume 1/n.log|{\rho}_n| tends to L. If L {\leq} log 2, they equidistribute on the boundary of the Mandelbrot set. If L > log 2 they equidistribute on the equipotential of the Mandelbrot set of level 2L - 2 log 2.
Cite
@article{arxiv.1306.2736,
title = {Quadratic polynomials, multipliers and equidistribution},
author = {Xavier Buff and Thomas Gauthier},
journal= {arXiv preprint arXiv:1306.2736},
year = {2013}
}