Global solvability for involutive systems on the torus
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 p...
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| Format: | Article |
| Language: | English |
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Texas State University
2013-11-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2013/244/abstr.html |
| _version_ | 1819132583007485952 |
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| author | Cleber de Medeira |
| author_facet | Cleber de Medeira |
| author_sort | Cleber de Medeira |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-22T09:33:42Z |
| format | Article |
| id | doaj.art-1c278cec797f4ce5adf95b3db943bd0a |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-22T09:33:42Z |
| publishDate | 2013-11-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-1c278cec797f4ce5adf95b3db943bd0a2022-12-21T18:30:52ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912013-11-012013244,18Global solvability for involutive systems on the torusCleber de Medeira0 Federal Univ. of Parana, Curitiba, Brazil 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.http://ejde.math.txstate.edu/Volumes/2013/244/abstr.htmlGlobal solvabilityinvolutive systemscomplex vector fieldsLiouville number |
| spellingShingle | Cleber de Medeira Global solvability for involutive systems on the torus Electronic Journal of Differential Equations Global solvability involutive systems complex vector fields Liouville number |
| title | Global solvability for involutive systems on the torus |
| title_full | Global solvability for involutive systems on the torus |
| title_fullStr | Global solvability for involutive systems on the torus |
| title_full_unstemmed | Global solvability for involutive systems on the torus |
| title_short | Global solvability for involutive systems on the torus |
| title_sort | global solvability for involutive systems on the torus |
| topic | Global solvability involutive systems complex vector fields Liouville number |
| url | http://ejde.math.txstate.edu/Volumes/2013/244/abstr.html |
| work_keys_str_mv | AT cleberdemedeira globalsolvabilityforinvolutivesystemsonthetorus |