Al-Ghassani, A;
Halburd, RG;
(2015)
Height growth of solutions and a discrete Painlevé equation.
Nonlinearity
, 28
(7)
pp. 2379-2396.
10.1088/0951-7715/28/7/2379.
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Abstract
Consider the discrete equation where the right side is of degree two in yn and where the coefficients an, bn and cn are rational functions of n with rational coefficients. Suppose that there is a solution such that for all sufficiently large n, yn ∈ ℚ and the height of yn dominates the height of the coefficient functions an, bn and cn. We show that if the logarithmic height of yn grows no faster than a power of n then either the equation is a well known discrete Painlevé equation dPII or its autonomous version or yn is also an admissible solution of a discrete Riccati equation. This provides further evidence that slow height growth is a good detector of integrability.
| Type: | Article |
|---|---|
| Title: | Height growth of solutions and a discrete Painlevé equation |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1088/0951-7715/28/7/2379 |
| Publisher version: | http://dx.doi.org/10.1088/0951-7715/28/7/2379 |
| Language: | English |
| Additional information: | Copyright © 2015 IOP Publishing Ltd & London Mathematical Society. |
| Keywords: | discrete Painleve equations, discrete integrable systems, Diophantine integrability |
| UCL classification: | UCL 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/1412350 |
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