H\"older continuity of core entropy for non-recurrent quadratic polynomials
Dynamical Systems
2024-10-17 v2
Abstract
We prove that core entropy is H\"older continuous as a function of external angles for a large class of quadratic polynomials that are non-recurrent with respect to angle-doubling, in particular all of them that exhibit a finite Hubbard tree. The result follows from a symbolic analysis of the Mandelbrot set and the dynamics of Hubbard trees in terms of kneading sequences which has been established in previous work.
Cite
@article{arxiv.2403.18109,
title = {H\"older continuity of core entropy for non-recurrent quadratic polynomials},
author = {Malte Hassler and Dierk Schleicher},
journal= {arXiv preprint arXiv:2403.18109},
year = {2024}
}
Comments
25 pages