Symmetry, singularities and integrability in complex dynamics I: the   reduction problem
  Quadratic systems generated using Yang-Baxter equations are integrable in a sense, but we display a deterioration in the possession of the Painlev\'e property as the number of equations in each `integrable system' increases. Certain intermediate systems are constructed and also tested for the Painlev\'e property. The Lie symmetries are also computed for completeness. 
Peter Leach, Spiros Cotsakis, George P. Flessas