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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the solvability of vector fields with real linear coefficients


Author: François Treves
Journal: Proc. Amer. Math. Soc. 137 (2009), 4209-4218
MSC (2000): Primary 35A07; Secondary 35F20
Published electronically: July 31, 2009
MathSciNet review: 2538582
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Abstract: The following result is proved: for a vector field with real linear coefficients to be locally solvable in $ \mathbb{R}^{n}$ it is necessary and sufficient that not all its orbits have a compact closure in the complement of the critical set of the vector field.


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Additional Information

François Treves
Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903-2101
Email: treves.jeanfrancois@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10033-3
PII: S 0002-9939(09)10033-3
Keywords: Vector fields, local solvability, foliations
Received by editor(s): April 14, 2009
Received by editor(s) in revised form: April 29, 2009
Published electronically: July 31, 2009
Communicated by: Bryna Kra
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.