Abstract
A paper of the author on the Levi-Civita problem, of mean motion (to appear in the Annali di Matematica) seems to lead to some contradictions with an important discovery by Denjoy, recently published in the Comptes Rendus. On combining the theorem of Denjoy with other results it will be shown in the present note that, in reality, those apparent contradictions do not exist at all. Let f(#, t) be a real-valued continuous function defined in the real (O, t) -plane and possessing the period 1 with respect to both # and t. Let T denote the closed orientable surface of genus one representing the fundamental domain 0 ? : < 1, 0 < t < 1. The function f should possess the additional property that the differential equation
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