TY  - JOUR
JF  - Nonlinearity
A1  - Al-Ghassani, A
A1  - Halburd, RG
UR  - http://dx.doi.org/10.1088/0951-7715/28/7/2379
SN  - 0951-7715
IS  - 7
N1  - Copyright © 2015 IOP Publishing Ltd & London Mathematical Society.
VL  - 28
SP  - 2379
KW  - discrete Painleve equations
KW  -  discrete integrable systems
KW  -  Diophantine integrability
N2  - 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 ? ? 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.
ID  - discovery1412350
TI  - Height growth of solutions and a discrete Painlevé equation
AV  - public
Y1  - 2015/07//
EP  - 2396
ER  -