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Rotations and integrability

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arxiv 2305.12370 v6 pith:QJELCBTI submitted 2023-05-21 nlin.SI math-phmath.DSmath.MP

A.V. Tsiganov This is my paper · ORCID
classification nlin.SImath-phmath.DSmath.MP
keywords integrableinvariantmotionrotationsadditionalalphacommutesdimensional
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abstract

We discuss some families of integrable and superintegrable systems in $n$-dimensional Euclidean space which are invariant to $m\geq n-2$ rotations. The integrable invariant Hamiltonian $H=\sum p_i^2+V(q)$ commutes with $n-2$ integrals of motion $M_\alpha $ and an additional integral of motion $G$, which are polynomials of first and fourth-order in momenta, respectively.

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Cited by 1 Pith paper

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  1. Integrable systems from Poisson reductions of generalized Hamiltonian torus actions

    math-ph 2025-07 unverdicted novelty 7.0 of 10

    Develops sufficient conditions for Poisson reduction of generalized Hamiltonian torus actions to preserve integrability and applies them to open problems on Lie group doubles and flat-connection moduli spaces.

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