Connection between the existence of first integrals and the painlevé property in two-dimensional lotka-volterra and quadratic systems

Taking advantage of the considerable amount of work done in the search for first integrals (invariants) for the two-dimensional Lotka-Volterra system and the quadratic system (lvs and qs), we compare the relations needed to exhibit invariants (one for the lvs, at least three for the qs) to the two conditions of the Painlevé test (index and compatibility). We find that, eventually restricting the invariants to those which are analytic (all exponents integers) and thereby adding new constraints, these constraints always coalesce with the two Painlevé conditions. We conclude that straightforward application of the Painlevé test picks up only these simple analytic invariants and that possession of the Painlevé property is too strong a condition for the existence of the invariants.

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