The generalized H\'enon-Heiles Hamiltonian
H=1/2(PX2​+PY2​+c1​X2+c2​Y2)+aXY2−bX3/3 with an additional
nonpolynomial term μY−2 is known to be Liouville integrable for three
sets of values of (b/a,c1​,c2​). It has been previously integrated by genus
two theta functions only in one of these cases. Defining the separating
variables of the Hamilton-Jacobi equations, we succeed here, in the two other
cases, to integrate the equations of motion with hyperelliptic functions.Comment: LaTex 2e. To appear, Journal of Mathematical Physic