Parameter scaling for the Fibonacci point
Dynamical Systems
2016-09-06 v1
Abstract
We prove geometric and scaling results for the real Fibonacci parameter value in the quadratic family . The principal nest of the Yoccoz parapuzzle pieces has rescaled asymptotic geometry equal to the filled-in Julia set of . The modulus of two such successive parapuzzle pieces increases at a linear rate. Finally, we prove a ``hairiness" theorem for the Mandelbrot set at the Fibonacci point when rescaling at this rate.
Cite
@article{arxiv.math/9606218,
title = {Parameter scaling for the Fibonacci point},
author = {Leroy Wenstrom},
journal= {arXiv preprint arXiv:math/9606218},
year = {2016}
}