We consider here the problem of the existence of a quasi-invariant which is linear in the momenta for Hamiltonians in three degrees of freedom. We show that such quasi-invariants are more constrained in their structure than in the two degrees of freedom case. We also show that some of these quasi-invariants have to be interpreted as ‘pseudo-translations’, i.e., as translations in a non-orthogonal system of coordinates.
Volume 94, 2020
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