Geodesic
Two integrable systems with integrals of motion of degree four
Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 3, pp. 443-455

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We discuss the possibility of using second-order Killing tensors to construct Liouville-integrable Hamiltonian systems that are not Nijenhuis integrable. As an example, we consider two Killing tensors with a nonzero Haantjes torsion that satisfy weaker geometric conditions and also three-dimensional systems corresponding to them that are integrable in Euclidean space and have two quadratic integrals of motion and one fourth-order integral in momenta.
Keywords: Hamilton–Jacobi equation, separation of variables, Killing tensor. 
@article{TMF_2016_186_3_a6,
     author = {A. V. Tsiganov},
     title = {Two integrable systems with integrals of motion of degree four},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {443--455},
     publisher = {mathdoc},
     volume = {186},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_186_3_a6/}
}
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A. V. Tsiganov. Two integrable systems with integrals of motion of degree four. Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 3, pp. 443-455. http://geodesic.mathdoc.fr/item/TMF_2016_186_3_a6/