Comment on "Optimal Periodic Orbits of Chaotic Systems"

Details Comment on "Optimal Periodic Orbits of Chaotic Systems" Comment on "Optimal Periodic Orbits of Chaotic Systems"

1997-06-27

arxiv.org/abs/chao-dyn/9707001v1

Nonlinear Sciences

Chaotic Dynamics

One Page, 1 Figure, Double Column format. Submitted to Physical Review Letters

Scientific paper

10.1103/PhysRevLett.80.1790

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.

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