Parametrization of phase space of Painlevé V equation

All Painlevé equations can be considered as Hamiltonian systems. Their phase spaces are some algebraic symplectic manifolds. We consider the simplest Painlevé equation corresponding to the isomonodromic deformation of the differential system with irregular singularity. The presented theory explains the presence of the symplectic structure and gives a method of the canonical parametrization of the phase space.