Some properties of the<i>k</i>-dimensional Lyness' map
Some properties of the<i>k</i>-dimensional Lyness' map
This paper is devoted to study some properties of the k-dimensional Lyness' map F(x1, ..., xk) = (x2, ..., xk, (a + ∑ki=2xi)/x1). Our main result presents a rational vector field that gives a Lie symmetry for F. This vector field is used, for k ⩽ 5, to give information …