The Weekly Workshop of the Cluster Geometry Laboratory. Speaker: Anton Dzhamay (University of Northern Colorado, USA)

Different Hamiltonians for Painlevé equations and their identification using geometry of the space of initial conditions

It is well-known that differential Painlevé 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 Painlevé 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 the Okamoto-Sakais geometric approach to Painlevé equations. We explain this approach mainly using the differential P-IV equation as an example, but the procedure is general and can be easily adapted to other Painlevé equations as well.
This is a joint work with Galina Filipuk, Adam Ligeza and Alex Stokes.

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