Abstract :
We further consider the n-dimensional ladder system, that is the homogeneous quadratic system of
first-order differential equations of the form ˙xi = xi n
j=1 aij xj , i = 1,n, where (aij ) = (i+1−j),
i, j = 1,n introduced by Imai and Hirata (nlin.SI/0212007). We establish the most general system of
first-order ordinary differential equations invariant under the algebra which characterises the ladder
system of Imai and Hirata and the algebra of minimal dimension required to specify completely
this most general system. We provide the complete symmetry group of the generalised hyperladder
system and discuss its integrability.
2004 Elsevier Inc. All rights reserved.
