Limit Distribution of Averages over Unstable Periodic Orbits Forming Chaotic Attractor
Chaotic Dynamics
2012-08-09 v1
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.
Keywords
Cite
@article{arxiv.1208.1691,
title = {Limit Distribution of Averages over Unstable Periodic Orbits Forming Chaotic Attractor},
author = {Denis S. Goldobin},
journal= {arXiv preprint arXiv:1208.1691},
year = {2012}
}