ω-limit sets from nonrecurrent points of flows on manifolds

In this paper we give a topological characterization of ω-limit sets from nonrecurrent points of flows on manifolds. This characterization is an extension of the one obtained for surfaces in [V. Jiménez López, G. Soler López, Accumulation points of nonrecurrent orbits of surface flows, Topology Appl. 137 (2004) 187–194]. However the result is not stated in the same terms. e case of the m-dimensional sphere we already gave a topological description of ω-limit sets of nonrecurrent points in [V. Jiménez López, G. Soler López, A characterization of ω-limit sets of non-recurrent orbits in S n , Internat. J. Bifur. Chaos Appl. Sci. Engrg. 13 (2001) 1727–1732]. This description generalized Vinograd Theorem, but it was only proved for the standard differential structure of S m . In this note we will obtain the same characterization for all differentiable structures as an easy consequence of the main result.