@unpublished{51206,
  abstract     = {{We present a numerical algorithm for the computation of invariant Ruelle
distributions on convex co-compact hyperbolic surfaces. This is achieved by
exploiting the connection between invariant Ruelle distributions and residues
of meromorphically continued weighted zeta functions established by the authors
together with Barkhofen (2021). To make this applicable for numerics we express
the weighted zeta as the logarithmic derivative of a suitable parameter
dependent Fredholm determinant similar to Borthwick (2014). As an additional
difficulty our transfer operator has to include a contracting direction which
we account for with techniques developed by Rugh (1992). We achieve a further
improvement in convergence speed for our algorithm in the case of surfaces with
additional symmetries by proving and applying a symmetry reduction of weighted
zeta functions.}},
  author       = {{Schütte, Philipp and Weich, Tobias}},
  booktitle    = {{arXiv:2308.13463}},
  title        = {{{Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions}}},
  year         = {{2023}},
}

@article{53410,
  abstract     = {{<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       = {{Delarue, Benjamin and Schütte, Philipp and Weich, Tobias}},
  issn         = {{1424-0637}},
  journal      = {{Annales Henri Poincaré}},
  keywords     = {{Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics}},
  number       = {{2}},
  pages        = {{1607--1656}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models}}},
  doi          = {{10.1007/s00023-023-01379-x}},
  volume       = {{25}},
  year         = {{2023}},
}

@article{31059,
  abstract     = {{In this article we prove meromorphic continuation of weighted zeta functions in the framework of open hyperbolic systems by using the meromorphically continued restricted resolvent of Dyatlov and Guillarmou (2016). We obtain a residue formula proving equality between residues of weighted zetas and invariant Ruelle distributions. We combine this equality with results of Guillarmou, Hilgert and Weich (2021) in order to relate the residues to Patterson-Sullivan distributions. Finally we provide proof-of-principle results concerning the numerical calculation of invariant Ruelle distributions for 3-disc scattering systems.}},
  author       = {{Schütte, Philipp and Weich, Tobias and Barkhofen, Sonja}},
  journal      = {{Communications in Mathematical Physics}},
  pages        = {{655--678}},
  title        = {{{Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems}}},
  doi          = {{https://doi.org/10.1007/s00220-022-04538-z}},
  volume       = {{398}},
  year         = {{2023}},
}

@article{31057,
  abstract     = {{In this paper we give an overview over some aspects of the modern mathematical theory of Ruelle resonances for chaotic, i.e. uniformly hyperbolic, dynamical systems and their implications in physics. First we recall recent developments in the mathematical theory of resonances, in particular how invariant Ruelle distributions arise as residues of weighted zeta functions. Then we derive a correspondence between weighted and semiclassical zeta functions in the setting of negatively curved surfaces. Combining this with results of Hilgert, Guillarmou and Weich yields a high frequency interpretation of invariant Ruelle distributions as quantum mechanical matrix coefficients in constant negative curvature. We finish by presenting numerical calculations of phase space distributions in the more physical setting of 3-disk scattering systems.}},
  author       = {{Barkhofen, Sonja and Schütte, Philipp and Weich, Tobias}},
  journal      = {{Journal of Physics A: Mathematical and Theoretical}},
  number       = {{24}},
  publisher    = {{IOP Publishing Ltd}},
  title        = {{{Semiclassical formulae For Wigner distributions}}},
  doi          = {{10.1088/1751-8121/ac6d2b}},
  volume       = {{55}},
  year         = {{2022}},
}

@unpublished{31058,
  abstract     = {{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 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.}},
  author       = {{Schütte, Philipp and Weich, Tobias and Delarue, Benjamin}},
  title        = {{{Resonances and weighted zeta functions for obstacle scattering via smooth models}}},
  year         = {{2021}},
}

@misc{31302,
  author       = {{Schütte, Philipp}},
  title        = {{{Numerically Investigating Residues of Weighted Zeta Functions on Schottky Surfaces}}},
  year         = {{2019}},
}

@misc{31301,
  author       = {{Schütte, Philipp}},
  title        = {{{Identifying and Realizing Symmetries in Quantum Walks - Symmetry Classes and Quantum Walks}}},
  year         = {{2017}},
}