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Hamiltonian integrable systems in a magnetic field and Symplectic-Haantjes geometry

Ond\v{r}ej Kub\r{u}Daniel ReyesPiergiulio TempestaGiorgio Tondo
Jan 2024
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摘要原文
We investigate the geometry of classical Hamiltonian systems immersed in a magnetic field in three-dimensional Riemannian configuration spaces. We prove that these systems admit non-trivial symplectic-Haantjes manifolds, which are symplectic manifolds endowed with an algebra of Haantjes (1,1)-tensors. These geometric structures allow us to determine separation variables for known systems algorithmically; besides, the underlying St\"ackel geometry is used to construct new families of integrable Hamiltonian models immersed in a magnetic field.
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