Comment on 'Time-averaged properties of unstable periodic orbits and chaotic orbits in ordinary differential equation systems'

摘要

The recent paper claims that mean characteristics of chaotic orbits differfrom the corresponding values averaged over the set of unstable periodicorbits, embedded in the chaotic attractor. We demonstrate that the allegeddiscrepancy is an artifact of the improper averaging: Since the natural measureis non-uniformly distributed over the attractor, different periodic orbits makedifferent contributions into the time averages. As soon as the correspondingweights are accounted for, the discrepancy disappears.