Abstract:
It is well known that on every compact 3-manifold there is a $C^1$ flow displaying a singular-hyperbolic isolated set which has no periodic orbits. By contrast, in this paper we prove that every singular-hyperbolic attracting set of a $C^1$ flow on a compact 3-manifold has a periodic orbit.
Key words and phrases:Singular-hyperbolic set, attracting set, periodic orbit.