Discrete mathematical modelling seminar

Seminar information archive ~08/16Next seminarFuture seminars 08/17~

Organizer(s) Tetsuji Tokihiro, Ralph Willox

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15:00-16:00   Room #117 (Graduate School of Math. Sci. Bldg.)
Anton Dzhamay (University of Northern Colorado)
Different Hamiltonians for Painlevé Equations and their identification using geometry of the space of
initial conditions (English)
[ Abstract ]
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-Sakai geometric approach to Painlevé equations. We explain this approach 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. (Joint work with Galina Filipuk, Adam Ligeza and Alexander Stokes.)