Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, Israel.
Phys Rev Lett. 2012 Feb 10;108(6):060604. doi: 10.1103/PhysRevLett.108.060604.
Weakly chaotic nonlinear maps with marginal fixed points have an infinite invariant measure. Time averages of integrable and nonintegrable observables remain random even in the long time limit. Temporal averages of integrable observables are described by the Aaronson-Darling-Kac theorem. We find the distribution of time averages of nonintegrable observables, for example, the time average position of the particle, x[over ¯]. We show how this distribution is related to the infinite invariant density. We establish four identities between amplitude ratios controlling the statistics of the problem.
具有边界不动点的弱混沌非线性映射具有无限不变测度。即使在长时间限制下，可积和不可积可观测量的时间平均值仍然是随机的。可积可观测量的时间平均值由 Aaronson-Darling-Kac 定理描述。我们找到不可积可观测量的时间平均值的分布，例如，粒子的时间平均位置 x[over ¯]。我们展示了这个分布如何与无限不变密度相关。我们建立了控制问题统计的四个振幅比之间的关系。
