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

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arxiv 2403.18109 v2 pith:3TJBD2BI submitted 2024-03-26 math.DS

Malte Hassler , Dierk Schleicher This is my paper · ORCID
classification math.DS
keywords coreentropyhubbardnon-recurrentolderpolynomialsquadraticanalysis
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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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