Halburd, RG;
Korhonen, RJ;
(2019)
Three approaches to detecting discrete integrability.
Computational Methods and Function Theory
, 19
(2)
pp. 299-313.
10.1007/s40315-019-00271-2.
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Abstract
A class of discrete equations is considered from three perspectives corresponding to three measures of the complexity of solutions: the (hyper-) order of meromorphic solutions in the sense of Nevanlinna, the degree growth of iterates over a function field and the height growth of iterates over the rational numbers. In each case, low complexity implies a form of singularity confinement which results in a known discrete Painlev\'e equation.
| Type: | Article |
|---|---|
| Title: | Three approaches to detecting discrete integrability |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s40315-019-00271-2 |
| Publisher version: | https://doi.org/10.1007/s40315-019-00271-2 |
| Language: | English |
| Additional information: | Copyright information © The Author(s) 2019 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
| Keywords: | Discrete Painlevé equations, Algebraic entropy, Order of meromorphic solutionn, Diophantine integrability |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10084548 |
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