Speiser meets Misiurewicz
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917604924325888 |
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| author | Aspenberg, Magnus Cui, Weiwei |
| author_facet | Aspenberg, Magnus Cui, Weiwei |
| contents | We propose a notion of Misiurewicz condition for transcendental entire functions and study perturbations of Speiser functions satisfying this condition in their parameter spaces (in the sense of Eremenko and Lyubich). We show that every Misiurewicz entire function can be approximated by hyperbolic maps in the same parameter space. Moreover, Misiurewicz functions are Lebesgue density points of hyperbolic maps if their Julia sets have zero Lebesgue measure. We also prove that the set of Misiurewicz Speiser functions has Lebesgue measure zero in the parameter space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_00385 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Speiser meets Misiurewicz Aspenberg, Magnus Cui, Weiwei Dynamical Systems Complex Variables 37F10, 30D05 We propose a notion of Misiurewicz condition for transcendental entire functions and study perturbations of Speiser functions satisfying this condition in their parameter spaces (in the sense of Eremenko and Lyubich). We show that every Misiurewicz entire function can be approximated by hyperbolic maps in the same parameter space. Moreover, Misiurewicz functions are Lebesgue density points of hyperbolic maps if their Julia sets have zero Lebesgue measure. We also prove that the set of Misiurewicz Speiser functions has Lebesgue measure zero in the parameter space. |
| title | Speiser meets Misiurewicz |
| topic | Dynamical Systems Complex Variables 37F10, 30D05 |
| url | https://arxiv.org/abs/2209.00385 |