Hölder continuity of core entropy for non-recurrent quadratic polynomials
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929545527951360 |
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| author | Hassler, Malte Schleicher, Dierk |
| author_facet | Hassler, Malte Schleicher, Dierk |
| contents | We prove that core entropy is Hölder 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18109 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hölder continuity of core entropy for non-recurrent quadratic polynomials Hassler, Malte Schleicher, Dierk Dynamical Systems 37F10, 37B40, 37F20, 37B10, 37E25 We prove that core entropy is Hölder 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. |
| title | Hölder continuity of core entropy for non-recurrent quadratic polynomials |
| topic | Dynamical Systems 37F10, 37B40, 37F20, 37B10, 37E25 |
| url | https://arxiv.org/abs/2403.18109 |