Planar polynomial foliations
Stephen Schecter and Michael F. Singer
Proc. Amer. Math. Soc. 79 (1980), 649-656
Primary 58F18; Secondary 57R30
Proc. Amer. Math. Soc. 83 (1981), 220.
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Abstract: Let and be two real polynomials of degree with no common real zeros. The solution curves of the vector field give a foliation of the plane. The leaf space of this foliation may not be a hausdorff space: there may be leaves L, which cannot be separated by open sets. We show that the number of such leaves is at most 2n and construct an example, for each even , of a planar polynomial foliation of degree n whose leaf space contains such leaves.
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