A Class of Vectorfields on S2 That Are Topologically Equivalent to Polynomial Vectorfields*

Let X be a C’ vectorfield on S* = {(x, y, z) E iw3: x2 +y2 + z2 = 1 } such that no open subset of S* is the union of closed orbits of X. If X has only a finite number of singular orbits and satisfies one additional condition, then it is shown that X is topologically equivalent to a polynomial vectorfield. A corollary is that a foliation 9 of the plane is topologically equivalent to a foliation by orbits of a polynomial vectorfield if and only if F has only a finite number of inseparable leaves. CD 1985