Levitin, M and Strohmaier, A orcid.org/0000-0002-8446-3840 (2021) Computations of Eigenvalues and Resonances on Perturbed Hyperbolic Surfaces with Cusps. International Mathematics Research Notices, 2021 (6). pp. 4003-4050. ISSN 1073-7928
Abstract
In this paper we describe a simple method that allows for a fast direct computation of the scattering matrix for a surface with hyperbolic cusps from the Neumann-to-Dirichlet map on the compact manifold with boundary obtained by removing the cusps. We illustrate that even if the Neumann-to-Dirichlet map is obtained by a finite element method (FEM) one can achieve good accuracy for the scattering matrix. We give various interesting examples of how this can be used to investigate the behaviour of resonances under conformal perturbations or when moving in Teichmüller space. For example, based on numerical experiments we rediscover the four arithmetic surfaces of genus one with one cusp. This demonstrates that it is possible to identify arithmetic objects using FEM. All the videos accompanying this paper are available with its online version, or externally either at michaellevitin.net/hyperbolic.html or as a dedicated YouTubeplaylist.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2019. Published by Oxford University Press. All rights reserved. This is an author produced version of an article published in International Mathematics Research Notices. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 13 Jun 2019 09:48 |
Last Modified: | 26 Jan 2022 18:04 |
Status: | Published |
Publisher: | Oxford University Press |
Identification Number: | 10.1093/imrn/rnz157 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:147183 |