On the number of poles of the dynamical zeta functions for billiard flow
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912234962157568 |
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| author | Petkov, Vesselin |
| author_facet | Petkov, Vesselin |
| contents | We study the number of the poles of the meromorphic continuation of the dynamical zeta functions $η_N$ and $η_D$ for several strictly convex disjoint obstacles satisfying non-eclipse condition. We obtain a strip $\{z \in \mathbb C:\: {\rm Re}\: s > β\}$ with infinite number of poles. For $η_D$ we prove the same result assuming the boundary real analytic. Moreover, for $η_N$ we obtain a characterisation of $β$ by the pressure $P(2G)$ of some function $G$ on the space $Σ_A^f$ related to the dynamical characteristics of the obstacle. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_17304 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the number of poles of the dynamical zeta functions for billiard flow Petkov, Vesselin Dynamical Systems 37D20, 37D05, 37D40, 11M41, 11M36 We study the number of the poles of the meromorphic continuation of the dynamical zeta functions $η_N$ and $η_D$ for several strictly convex disjoint obstacles satisfying non-eclipse condition. We obtain a strip $\{z \in \mathbb C:\: {\rm Re}\: s > β\}$ with infinite number of poles. For $η_D$ we prove the same result assuming the boundary real analytic. Moreover, for $η_N$ we obtain a characterisation of $β$ by the pressure $P(2G)$ of some function $G$ on the space $Σ_A^f$ related to the dynamical characteristics of the obstacle. |
| title | On the number of poles of the dynamical zeta functions for billiard flow |
| topic | Dynamical Systems 37D20, 37D05, 37D40, 11M41, 11M36 |
| url | https://arxiv.org/abs/2407.17304 |