{"abstract":[{"lang":"eng","text":"We present a numerical algorithm for the computation of invariant Ruelle\r\ndistributions on convex co-compact hyperbolic surfaces. This is achieved by\r\nexploiting the connection between invariant Ruelle distributions and residues\r\nof meromorphically continued weighted zeta functions established by the authors\r\ntogether with Barkhofen (2021). To make this applicable for numerics we express\r\nthe weighted zeta as the logarithmic derivative of a suitable parameter\r\ndependent Fredholm determinant similar to Borthwick (2014). As an additional\r\ndifficulty our transfer operator has to include a contracting direction which\r\nwe account for with techniques developed by Rugh (1992). We achieve a further\r\nimprovement in convergence speed for our algorithm in the case of surfaces with\r\nadditional symmetries by proving and applying a symmetry reduction of weighted\r\nzeta functions."}],"publication":"arXiv:2308.13463","title":"Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions","date_updated":"2024-02-11T19:56:01Z","language":[{"iso":"eng"}],"department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"type":"preprint","citation":{"bibtex":"@article{Schütte_Weich_2023, title={Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions}, journal={arXiv:2308.13463}, author={Schütte, Philipp and Weich, Tobias}, year={2023} }","ieee":"P. Schütte and T. Weich, “Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions,” <i>arXiv:2308.13463</i>. 2023.","ama":"Schütte P, Weich T. Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions. <i>arXiv:230813463</i>. Published online 2023.","short":"P. Schütte, T. Weich, ArXiv:2308.13463 (2023).","apa":"Schütte, P., &#38; Weich, T. (2023). Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions. In <i>arXiv:2308.13463</i>.","mla":"Schütte, Philipp, and Tobias Weich. “Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions.” <i>ArXiv:2308.13463</i>, 2023.","chicago":"Schütte, Philipp, and Tobias Weich. “Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions.” <i>ArXiv:2308.13463</i>, 2023."},"user_id":"49178","year":"2023","author":[{"first_name":"Philipp","id":"50168","last_name":"Schütte","full_name":"Schütte, Philipp"},{"first_name":"Tobias","id":"49178","full_name":"Weich, Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919"}],"external_id":{"arxiv":["2308.13463"]},"date_created":"2024-02-06T20:58:35Z","status":"public","_id":"51206"}