ω-limit sets from nonrecurrent points of flows on manifolds

AbstractIn 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.For the 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 Sn, 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 Sm. In this note we will obtain the same characterization for all differentiable structures as an easy consequence of the main result