4 research outputs found
Some properties of the k-dimensional Lyness' map
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.Comment: 22 pages; 3 figure