Rotations and Integrability

We discuss some families of integrable and superintegrable systems in \(n\) -dimensional Euclidean space which are invariant under \(m\geqslant n-2\) rotations. The invariant Hamiltonian \(H=\sum p_{i}^{2}+V(q)\) is integrable with \(n-2\) integrals of motion \(M_{\alpha}\) and an additional integral ofmotion \(G\) , which are first- and fourth-order polynomials in momenta, respectively.