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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2205.11408 |
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| _version_ | 1866913525454077952 |
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| author | Fu, Yuqiu |
| author_facet | Fu, Yuqiu |
| contents | We prove that the dynamical zeta function $Z(s)$ associated to $z^2 + c$ with $c < -3.75$ has essential zero-free strips of size $1/2 +$, that is, for every $ε> 0$, there exist only finitely many zeros in the strip $\mathrm{Re}(s) > 1/2 + ε$. We also present some numerical plots of zeros of $Z(s)$ using the method proposed in Jenkinson-Pollicott. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_11408 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Zeros of dynamical zeta functions for hyperbolic quadradic maps Fu, Yuqiu Dynamical Systems We prove that the dynamical zeta function $Z(s)$ associated to $z^2 + c$ with $c < -3.75$ has essential zero-free strips of size $1/2 +$, that is, for every $ε> 0$, there exist only finitely many zeros in the strip $\mathrm{Re}(s) > 1/2 + ε$. We also present some numerical plots of zeros of $Z(s)$ using the method proposed in Jenkinson-Pollicott. |
| title | Zeros of dynamical zeta functions for hyperbolic quadradic maps |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2205.11408 |