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- W20199705 abstract "We determine all the $${mathcal{C}^1}$$ planar vector fields with a given set of orbits of the form y − y(x) = 0 satisfying convenient assumptions. The case when these orbits are branches of an algebraic curve is also study. We show that if a quadratic vector field admits a unique irreducible invariant algebraic curve $${g(x, y) = sum_{j=0}^S a_j(x) y^{S-j}= 0}$$ with S branches with respect to the variable y, then the degree of the polynomial g is at most 4S." @default.
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- W20199705 date "2011-07-13" @default.
- W20199705 modified "2023-10-17" @default.
- W20199705 title "Planar Vector Fields with a Given Set of Orbits" @default.
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- W20199705 doi "https://doi.org/10.1007/s10884-011-9219-0" @default.
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