Some properties of the k-dimensional Lyness' map

Details Some properties of the k-dimensional Lyness' map Some properties of the k-dimensional Lyness' map

2008-01-28

arxiv.org/abs/0801.4360v1

J. of Physics A: Mathematical & Theoretical 41 (2008) 285205

Mathematics

Dynamical Systems

22 pages; 3 figures

Scientific paper

10.1088/1751-8113/41/28/285205

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.

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