Open AccessGlobal solutions to involutive systems
Author(s) -
Adalberto P. Bergamasco,
Alexandre Kirilov,
Wagner Vieira Leite Nunes,
Sérgio Luís Zani
Publication year - 2015
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc/12633
Subject(s) - algorithm , annotation , computer science , artificial intelligence
In this work we consider a class of systems of two vector fields on the 3-torus associated to a closed smooth complex 1-form c = a + ib with b exact. Necessary conditions and sufficient conditions for this system to be globally solvable are provided in terms of the position of the global extrema and the connectedness of sublevel and superlevel sets of the primitives of b, together with arithmetical properties of the periods of a.CNPqFAPES