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arXiv · 2403.18109

H\"older continuity of core entropy for non-recurrent quadratic polynomials

Malte Hassler·Dierk Schleicher
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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.

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Malte Hassler, Dierk Schleicher. 2024-03-26. H\"older continuity of core entropy for non-recurrent quadratic polynomials. https://arxiv.org/abs/2403.18109

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