Systematic construction of nonautonomous Hamiltonian equations of Painlevé type. I. Frobenius integrability
[ 1 ] Instytut Matematyki, Wydział Automatyki, Robotyki i Elektrotechniki, Politechnika Poznańska | [ P ] employee
2022
scientific article
english
- Frobenius integrability
- nonautonomous Hamiltonian equations
- Painlevé equations
- Stäckel systems
EN This article is the first one in a suite of three articlesexploring connections between dynamical systems ofStäckel type and of Painlevé type. In this article, wepresent a deformation of autonomous Stäckel-type sys-tems to nonautonomous Frobenius integrable systems.First, we consider quasi-Stäckel systems with quadraticin momenta Hamiltonians containing separable poten-tials with time-dependent coefficients, and then, wepresent a procedure of deforming these equations tononautonomous Frobenius integrable systems. Then,we present a procedure of deforming quasi-Stäckel sys-tems with so-called magnetic separable potentials tononautonomous Frobenius integrable systems. We alsoprovide a complete list of all two- and three-dimensionalFrobenius integrable systems, both with ordinary andwith magnetic potentials, which originate in our con-struction. Further, we prove the equivalence betweenboth classes of systems. Finally, we show how Painlevéequations 𝑃𝐼−𝑃𝐼𝑉 can be derived from our scheme.
12.12.2021
1208 - 1250
100
2,7