Non-uniformly hyperbolic flows and shadowing

We consider a hyperbolic ergodic measure of a C1C1 flow on a compact manifold. Under the hypothesis that there are no fixed points and that the Oseledec splitting of the normal bundle satisfies a limit domination property, we prove that the measure has a shadowing property. As an application of this result we prove that the measure can be approached on the weak⁎ topology by measures supported on hyperbolic periodic orbits.