Abstract

We consider a class of systems of two smooth vector fields on the 3-torus associated to a closed 1-form. The global solvability of such systems is completely determined by the connectedness of the sublevel and superlevel sets of a primitive of this 1-form in the minimal covering. The main point of this talk is addressing the case when the 1-form is non-exact and its periods are rationally dependent. This is a work in collaboration with A. Bergamasco, A. Kirilov, and W. Nunes.

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