On graphical foliations and the global existence of Euler's multiplier

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We present an equivalent criterion for the global existence of Euler's multiplier for an integrable one-form taking into account the corresponding codim-1-foliation. In particular, the impact of inseparable leaves is considered. Here, we suppose that the foliation can be reduced to a graph; we also discuss obstructions for this assumption. The properties of this graph are decisive for the global existence of Euler's multiplier. As applications we investigate some special cases in which the graph turns out to look very simple.
28 pages, 10 figures; some sections added or completely rewritten

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Geometric Topology, Classical Analysis and ODEs, 57R30; 58F18

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http://salesiana.dossiersoluciones.com/handle/123456789/223748

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0108153
 http://arxiv.org/abs/math/0108153

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arXiv