On volume preserving almost Anosov flows

We call a flow on a compact manifold "almost Anosov'' if the Anosov property of being hyperbolic everywhere is violated at (a finite collection of) periodic solutions. In this talk, I will present results on what happens if the flow (on a 3-manifold) preserves volume and has a periodic orbit of neutral saddle type. Asymptotics of the resulting intermittent behaviour can be accurate estimated and give rise to (non-standard) Central Limit Theorem or Stable Laws for such flows.