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On the global solvability of involutive systems. (English) Zbl 1359.37107
Summary: We consider a class of involutive systems in \(\mathbb{T}^{n + 1}\) associated with a closed 1-form defined on the torus \(\mathbb{T}^n\). We prove that, under a geometric condition, the global solvability of this class is equivalent to a diophantine condition involving Liouville forms and the connectedness of all sublevel and superlevel sets of a global primitive associated with the system.

MSC:
37F75 Dynamical aspects of holomorphic foliations and vector fields
32M25 Complex vector fields, holomorphic foliations, \(\mathbb{C}\)-actions
35S05 Pseudodifferential operators as generalizations of partial differential operators
35F05 Linear first-order PDEs
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