article published Benjamin Delarue author 70575 Philipp Schütte author 50168 Tobias Weich author 491780000-0002-9648-6919 548 department <jats:title>Abstract</jats:title><jats:p>We consider a geodesic billiard system consisting of a complete Riemannian manifold and an obstacle submanifold with boundary at which the trajectories of the geodesic flow experience specular reflections. We show that if the geodesic billiard system is hyperbolic on its trapped set and the latter is compact and non-grazing, the techniques for open hyperbolic systems developed by Dyatlov and Guillarmou (Ann Henri Poincaré 17(11):3089–3146, 2016) can be applied to a smooth model for the discontinuous flow defined by the non-grazing billiard trajectories. This allows us to obtain a meromorphic resolvent for the generator of the billiard flow. As an application we prove a meromorphic continuation of weighted zeta functions together with explicit residue formulae. In particular, our results apply to scattering by convex obstacles in the Euclidean plane.</jats:p> Springer Science and Business Media LLC2023 eng Mathematical PhysicsNuclear and High Energy PhysicsStatistical and Nonlinear Physics 1424-0637 1424-066110.1007/s00023-023-01379-x 2521607-1656 Delarue, Benjamin, Philipp Schütte, and Tobias Weich. “Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models.” <i>Annales Henri Poincaré</i> 25, no. 2 (2023): 1607–56. <a href="https://doi.org/10.1007/s00023-023-01379-x">https://doi.org/10.1007/s00023-023-01379-x</a>. B. Delarue, P. Schütte, T. Weich, Annales Henri Poincaré 25 (2023) 1607–1656. Delarue, B., Schütte, P., &#38; Weich, T. (2023). Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models. <i>Annales Henri Poincaré</i>, <i>25</i>(2), 1607–1656. <a href="https://doi.org/10.1007/s00023-023-01379-x">https://doi.org/10.1007/s00023-023-01379-x</a> B. Delarue, P. Schütte, and T. Weich, “Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models,” <i>Annales Henri Poincaré</i>, vol. 25, no. 2, pp. 1607–1656, 2023, doi: <a href="https://doi.org/10.1007/s00023-023-01379-x">10.1007/s00023-023-01379-x</a>. Delarue B, Schütte P, Weich T. Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models. <i>Annales Henri Poincaré</i>. 2023;25(2):1607-1656. doi:<a href="https://doi.org/10.1007/s00023-023-01379-x">10.1007/s00023-023-01379-x</a> @article{Delarue_Schütte_Weich_2023, title={Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models}, volume={25}, DOI={<a href="https://doi.org/10.1007/s00023-023-01379-x">10.1007/s00023-023-01379-x</a>}, number={2}, journal={Annales Henri Poincaré}, publisher={Springer Science and Business Media LLC}, author={Delarue, Benjamin and Schütte, Philipp and Weich, Tobias}, year={2023}, pages={1607–1656} } Delarue, Benjamin, et al. “Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models.” <i>Annales Henri Poincaré</i>, vol. 25, no. 2, Springer Science and Business Media LLC, 2023, pp. 1607–56, doi:<a href="https://doi.org/10.1007/s00023-023-01379-x">10.1007/s00023-023-01379-x</a>. 534102024-04-11T12:30:14Z2024-04-11T12:37:34Z