It is well-known that differential Painleve equations can be written in a Hamiltonian form. However, a coordinate form of such representation is far from unique -- there are many very different Hamiltonians that result in the same differential Painle
ve equation. In this paper we describe a systematic procedure of finding changes of coordinates transforming different Hamiltonian systems into some canonical form. Our approach is based on Sakais geometric theory of Painleve equations. We explain our approach using the fourth differential ${text{P}_{mathrm{IV}}}$ equation as an example, but it can be easily adapted to other Painleve equations as well.
