  We consider open billiards in the plane satisfying the no-eclipse condition.
We show that the points in the non-wandering set depend differentiably on
deformations to the boundary of the billiard. We use Bowen's equation to
estimate the Hausdorff dimension of the non-wandering set of the billiard.
Finally we show that the Hausdorff dimension depends differentiably on
sufficiently smooth deformations to the boundary of the billiard, and estimate
the derivative with respect to such deformations.
