The Eremenko-Lyubich constant
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866915053663420416 |
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| author | Rempe, Lasse |
| author_facet | Rempe, Lasse |
| contents | Eremenko and Lyubich proved that an entire function whose set of singular values is bounded is expanding at points where its image has large modulus. These expansion properties have been at the centre of the subsequent study of this class of functions, now called the Eremenko-Lyubich class. We improve the estimate of Eremenko and Lyubich, and show that the new estimate is asymptotically optimal. As a corollary, we obtain an elementary proof that functions in the Eremenko-Lyubich class have lower order at least $1/2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_09053 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The Eremenko-Lyubich constant Rempe, Lasse Complex Variables Dynamical Systems 30D15 (primary), 30D05, 37F10 (secondary) Eremenko and Lyubich proved that an entire function whose set of singular values is bounded is expanding at points where its image has large modulus. These expansion properties have been at the centre of the subsequent study of this class of functions, now called the Eremenko-Lyubich class. We improve the estimate of Eremenko and Lyubich, and show that the new estimate is asymptotically optimal. As a corollary, we obtain an elementary proof that functions in the Eremenko-Lyubich class have lower order at least $1/2$. |
| title | The Eremenko-Lyubich constant |
| topic | Complex Variables Dynamical Systems 30D15 (primary), 30D05, 37F10 (secondary) |
| url | https://arxiv.org/abs/2105.09053 |