Direct construction of a bi-Hamiltonian structure for cubic Hénon-Heiles systems (Q2226019)

The author claims that the problem of separation of variables in integrable Hamiltonian systems remains a topical area of research. One of the approaches to study such systems is a technique based on the so-called Kovalewski conditions [\textit{F. Magri}, ``The Kowalewski's top revisited'', Preprint, \url{arXiv:1809.01879}]. The author suggests a way to calculate directly the second compatible Hamiltonian structure for the cubic Hénon-Heiles system, thus providing the partition variables as eigenvalues of the recursive operation.