Perturbations of exponential maps: Non-recurrent dynamics
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
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| _version_ | 1866916425553149952 |
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| author | Aspenberg, Magnus Cui, Weiwei |
| author_facet | Aspenberg, Magnus Cui, Weiwei |
| contents | We study perturbations of non-recurrent parameters in the exponential family. It is shown that the set of such parameters has Lebesgue measure zero. This particularly implies that the set of escaping parameters has Lebesgue measure zero, which complements a result of Qiu from 1994. Moreover, we show that non-recurrent parameters can be approximated by hyperbolic ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_11093 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Perturbations of exponential maps: Non-recurrent dynamics Aspenberg, Magnus Cui, Weiwei Dynamical Systems 37F10, 30D05 We study perturbations of non-recurrent parameters in the exponential family. It is shown that the set of such parameters has Lebesgue measure zero. This particularly implies that the set of escaping parameters has Lebesgue measure zero, which complements a result of Qiu from 1994. Moreover, we show that non-recurrent parameters can be approximated by hyperbolic ones. |
| title | Perturbations of exponential maps: Non-recurrent dynamics |
| topic | Dynamical Systems 37F10, 30D05 |
| url | https://arxiv.org/abs/2206.11093 |