Planar polynomial foliations
Authors: Stephen Schecter and Michael F. Singer
Journal: Proc. Amer. Math. Soc. 79 (1980), 649-656
MSC: Primary 58F18; Secondary 57R30
Addendum: Proc. Amer. Math. Soc. 83 (1981), 220.
MathSciNet review: 572321
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.
Keywords: Planar polynomial vector field, foliation, inseparable leaves
Article copyright: © Copyright 1980 American Mathematical Society