---
_id: '53410'
abstract:
- lang: eng
  text: <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>
author:
- first_name: Benjamin
  full_name: Delarue, Benjamin
  id: '70575'
  last_name: Delarue
- first_name: Philipp
  full_name: Schütte, Philipp
  id: '50168'
  last_name: Schütte
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
citation:
  ama: 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>
  apa: 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>
  bibtex: '@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} }'
  chicago: '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>.'
  ieee: '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>.'
  mla: 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>.
  short: B. Delarue, P. Schütte, T. Weich, Annales Henri Poincaré 25 (2023) 1607–1656.
date_created: 2024-04-11T12:30:14Z
date_updated: 2024-04-11T12:37:34Z
department:
- _id: '548'
doi: 10.1007/s00023-023-01379-x
intvolume: '        25'
issue: '2'
keyword:
- Mathematical Physics
- Nuclear and High Energy Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
page: 1607-1656
publication: Annales Henri Poincaré
publication_identifier:
  issn:
  - 1424-0637
  - 1424-0661
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models
type: journal_article
user_id: '70575'
volume: 25
year: '2023'
...