Integrability properties of Kahan's method
  We present several novel examples of integrable quadratic vector fields for which Kahan's discretization method preserves integrability. Our examples include generalized Suslov and Ishii systems, Nambu systems, Riccati systems, and the first Painlev\'e equation. We also discuss how Manin transformations arise in Kahan discretizations of certain vector fields. 
Elena Celledoni, Robert I McLachlan, David I McLaren, Brynjulf Owren   and G R W Quispel
nlin.SI math.NA