%0 Journal Article
%T Some properties of the k-dimensional Lyness' map
%A Anna Cima
%A Armengol Gasull
%A Victor Manosa
%J Mathematics
%D 2008
%I arXiv
%R 10.1088/1751-8113/41/28/285205
%X This paper is devoted to study some properties of the k-dimensional Lyness' map. Our main result presentes a rational vector field that gives a Lie symmetry for F. This vector field is used, for k less or equal to 5 to give information about the nature of the invariant sets under F. When k is odd, we also present a new (as far as we know) first integral for F^2 which allows to deduce in a very simple way several properties of the dynamical system generated by F. In particular for this case we prove that, except on a given codimension one algebraic set, none of the positive initial conditions can be a periodic point of odd period.
%U http://arxiv.org/abs/0801.4360v1