Geodesic
An estimate from above of the number of invariant straight lines of $n$-th degree polynomial vector field
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 2, pp. 171-179

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It is shown that the $n$-th degree polynomial vector field in the plane has at most $2n + 1$ ($2n + 2$) invariant straight lines when $n$ is even (odd) and $n\geq 3$ if it has a singular point for which $n + 1$ invariant straight lines and $n$ parallel invariant straight lines with a certain angular coefficient are incident. 
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     title = {An estimate from above of the number of invariant straight lines of $n$-th degree polynomial vector field},
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V. B. Tlyachev; A. D. Ushkho; D. S. Ushkho. An estimate from above of the number of invariant straight lines of $n$-th degree polynomial vector field. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 2, pp. 171-179. http://geodesic.mathdoc.fr/item/ISU_2015_15_2_a6/