On rotation invariant integrable systems

A. V. Tsiganov

Izvestiya. Mathematics , Tome 88 (2024) no. 2, pp. 389-409.

Résumé

The problem of finding the first integrals of the Newton equations in the $n$-dimensional Euclidean space is reduced to that of finding two integrals of motion on the Lie algebra $\mathrm{so}(4)$ which are invariant under $m\geq n-2$ rotation symmetry fields. As an example, we obtain several families of integrable and superintegrable systems with first, second, and fourth-degree integrals of motion in the momenta. The corresponding Hamilton–Jacobi equation does not admit separation variables in any of the known curvilinear orthogonal coordinate systems in the Euclidean space.

Détail

Keywords: differential equation, first integral, symmetry field
Mots-clés : quartic invariant.

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