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arXiv · 0801.4360

Some properties of the k-dimensional Lyness' map

Anna Cima·Armengol Gasull·Victor Manosa
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Abstract

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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Anna Cima, Armengol Gasull, Victor Manosa. 2008-01-28. Some properties of the k-dimensional Lyness' map. https://doi.org/10.1088/1751-8113%2F41%2F28%2F285205

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