English

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.

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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}
}

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25 pages