CONNECTION BETWEEN THE EXISTENCE OF FIRST INTEGRALS AND THE PAINLEVE PROPERTY IN 2-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-Volter ra system and the quadratic system (LVS and QS), we compare the relati ons needed to exhibit invariants (one for the LVS; at least three for the Qs) to the two conditions of the Painleve test (index and compatib ility). We find that, eventually restricting the invariants to those w hich are analytic (all exponents integers) and thereby adding new cons traints, these constraints always coalesce with the two Painleve condi tions. We conclude that straight-forward application of the Painleve t est picks up only these simple analytic invariants and that possession of the Painleve property is too strong a condition for the existence of the invariants.