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

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

2009-12-03

arxiv.org/abs/0912.0596v1

Phys. Rev. E 81, 018201 (2010)

Physics

Condensed Matter

Statistical Mechanics

Comment, 2 pages, 1 figure

Scientific paper

10.1103/PhysRevE.81.018201

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

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