Hamiltonians associated with the third and fifth Painleve equations

摘要

We obtain a Painlev,-type differential equation for the simplest rational Hamiltonian associated with the fifth Painlev, equation in the case gamma not equal 0, delta = 0. We prove the existence of Hamiltonians of a nonrational type associated with the fifth Painlev, equation in the case gamma not equal 0, delta = 0. We obtain a generalization of the Garnier and Okamoto formulas for rational Hamiltonians associated with the third Painlev, tequation.