eprintid: 1412350
rev_number: 34
eprint_status: archive
userid: 608
dir: disk0/01/41/23/50
datestamp: 2013-10-31 20:59:44
lastmod: 2021-10-04 01:38:37
status_changed: 2016-03-31 12:09:14
type: article
metadata_visibility: show
item_issues_count: 0
creators_name: Al-Ghassani, A
creators_name: Halburd, RG
title: Height growth of solutions and a discrete Painlevé equation
ispublished: pub
divisions: UCL
divisions: B04
divisions: C06
divisions: F59
keywords: discrete Painleve equations, discrete integrable systems, Diophantine integrability
note: Copyright © 2015 IOP Publishing Ltd & London Mathematical Society.
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.
date: 2015-07
official_url: http://dx.doi.org/10.1088/0951-7715/28/7/2379
vfaculties: VMPS
oa_status: green
full_text_type: other
language: eng
primo: open
primo_central: open_green
verified: verified_manual
elements_source: Manually entered
elements_id: 912856
doi: 10.1088/0951-7715/28/7/2379
lyricists_name: Halburd, Rodney
lyricists_id: RHALB06
full_text_status: public
publication: Nonlinearity
volume: 28
number: 7
pagerange: 2379-2396
issn: 0951-7715
citation:        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 <https://doi.org/10.1088/0951-7715%2F28%2F7%2F2379>.       Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/1412350/1/Halburd_1601.03100v1.pdf