On the number of poles of the dynamical zeta functions for billiard flow
| Autor: | Petkov, Vesselin |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We study the number of the poles of the meromorphic continuation of the dynamical zeta functions $\eta_N$ and $\eta_D$ for several strictly convex disjoint obstacles satisfying non-eclipse condition. We obtain a strip $\{z \in \mathbb C:\: {\rm Re}\: s > \beta\}$ with infinite number of poles. For $\eta_D$ we prove the same result assuming the boundary real analytic. Moreover, for $\eta_N$ we obtain a characterisation of $\beta$ by the pressure $P(2G)$ of some function $G$ on the space $\Sigma_A^f$ related to the dynamical characteristics of the obstacle. Comment: We obtain new results without restriction on the abscissa of convergence $b_1$. We correct some misprints and notations |
| Databáze: | arXiv |
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