Electron. J. Diff. Equ., Vol. 2013 (2013), No. 244, pp. 1-8.

Global solvability for involutive systems on the torus

Cleber de Medeira

In this article, we consider a class of involutive systems of n smooth vector fields on the torus of dimension n+1. We prove that the global solvability of this class is related to an algebraic condition involving Liouville forms and the connectedness of all sublevel and superlevel sets of the primitive of a certain 1-form associated with the system.

Submitted April 19, 2013. Published November 8, 2013.
Math Subject Classifications: 35N10, 32M25.
Key Words: Global solvability; involutive systems; complex vector fields; Liouville number.

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Cleber de Medeira
Department of mathematics
Federal University of Paraná
19081, Curitiba, Brazil
email: clebermedeira@ufpr.br

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