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We address the question of representativeness of a single long unstableperiodic orbit for properties of the chaotic attractor it is embedded in. Y.Saiki and M. Yamada [Phys. Rev. E 79, 015201(R) (2009)] have recently suggestedthe hypothesis that there exist a limit distribution of averages over unstableperiodic orbits with given number of loops, N, which is not a Diracdelta-function for infinitely long orbits. In this paper we show that the limitdistribution is actually a delta-function and standard deviations decay as1/sqrt(N) for large enough N.

Limit Distribution of Averages over Unstable Periodic Orbits Forming Chaotic Attractor