Geodesic
Versal deformations of differential forms of real degree on the real line
Izvestiya. Mathematics , Tome 37 (1991) no. 3, pp. 525-537.

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A normal form is given for families of differential forms of nonzero real degree on the real line (in particular, a normal form for families of vector fields on the line), which depend smoothly on the parameters, in the neighborhood of zeros of the coefficient of the form of finite multiplicity (zeros of finite multiplicity of the field). 
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V. P. Kostov. Versal deformations of differential forms of real degree on the real line. Izvestiya. Mathematics , Tome 37 (1991) no. 3, pp. 525-537. http://geodesic.mathdoc.fr/item/IM2_1991_37_3_a3/

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