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Discrete mathematical modelling seminar
Seminar information archive ～09/11｜Next seminar｜Future seminars 09/12～
| Organizer(s) | Tetsuji Tokihiro, Ralph Willox |
|---|
2022/08/18
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)
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.)
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.)
