Abstract: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 of
motion $$G$$, which are first- and fourth-order polynomials in momenta, respectively.
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