Periodic orbits: the really big deal

In order to compute an exact unstable periodic solution, one needs to guess the initial 50,000-100,000 velocity fields with a sufficient accuracy that the exponentially unstable state of fluid recurs nearly exactly after an (initially unknown) period.

Until the first unstable periodic solutions of Navier-Stokes were computed by Kawahara in 2001, this seemed utterly out of reach.