Vassiliev invariants and writhe for periodic orbits of Axiom A flows

We obtain asymptotics for the average value taken by a Vassiliev invariant on knots appearing as periodic orbits of an Axiom A flow on $S^3\mathrm{.}$ The methods used also give asymptotics for the writhe of periodic orbits. Our results are analogous to those of G. Contreras for average linking numbers.