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arXiv · 1208.1691

Limit Distribution of Averages over Unstable Periodic Orbits Forming Chaotic Attractor

Denis S. Goldobin
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Abstract

We address the question of representativeness of a single long unstable periodic 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 suggested the hypothesis that there exist a limit distribution of averages over unstable periodic orbits with given number of loops, N, which is not a Dirac delta-function for infinitely long orbits. In this paper we show that the limit distribution is actually a delta-function and standard deviations decay as 1/sqrt(N) for large enough N.

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Denis S. Goldobin. 2012-08-08. Limit Distribution of Averages over Unstable Periodic Orbits Forming Chaotic Attractor. https://arxiv.org/abs/1208.1691

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