Rotations and integrability

Author:

A. V. Tsiganov

Keyword:

Nonlinear Sciences, Exactly Solvable and Integrable Systems, Exactly Solvable and Integrable Systems (nlin.SI), Mathematical Physics (math-ph), Dynamical Systems (math.DS)

journal:

date:

2023-05-20 16:00:00

Abstract

We discuss few families of integrable and superintegrable systems in $n$-dimensional Euclidean space, which are invariant to $m\geq n-2$ rotations. Invariant Hamiltonian $H=\sum p_i^2+V(q)$ and additional integral of motion $G$ are polynomials of second and fourth order in momenta, which can be obtained using various realizations of the Lie algebra $so(4)$.

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