Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 128, pp. 1-14.

Title: Existence of periodic orbits for vector fields
       via Fuller index and the averaging method

Authors: Pierluigi Benevieri (Univ. degli Studi di Firenze, Italy)
   Andrea Gavioli (Univ. degli Studi di Modena e Reggio Emilia,Italy)
   Massimo Villarini (Univ. degli Studi di Modena e Reggio Emilia,Italy)

Abstract: 
 We prove a  generalization of a theorem proved by
 Seifert and Fuller concerning the existence of periodic 
 orbits  of vector fields via the averaging method. 
 Also we show applications of these results to Kepler motion 
 and to  geodesic flows on spheres.
 
Submitted September 3, 2003. Published November 3, 2004.
Math Subject Classifications: 34C25, 34C29, 34C40, 37C10, 57R25.
Key Words: Vector fields on manifolds; periodic orbits; Fuller index.