Comment on "Optimal Periodic Orbits of Chaotic Systems"
In a recent Letter, Hunt and Ott argued that SHORT-period unstable periodic
orbits (UPOs) would be the invariant sets associated with a chaotic attractor
that are most likely to optimize the time average of some smooth scalar
performance function. In this Comment, we show that their conclusion does not
hold generally and that optimal time averages may specifically require
long-period UPOs. This situation can arise when long-period UPOs are able to
spend substantial amounts of time in a region of phase space that is close to
large values of the performance function.