论文标题
可集成标准地图的Cauchy分布
Cauchy distributions for the integrable standard map
论文作者
论文摘要
我们考虑了鉴于当前关于非理性旋转的急性总和的发展（零扰动）两维标准图，以及最近的数值证据表明它可能具有非平凡的Q-Gaussis统计。使用经典和最近的结果，我们表明，长时间和归一化后，轨道中心位置的总和的相位平均值服从Cauchy分布（Q-Gaussian Q = 2），而对于几乎所有单独的轨道来说，总和都不会遵守任何分布。我们讨论了KAM Tori的分布存在问题。
We consider the integrable (zero perturbation) two--dimensional standard map, in light of current developments on ergodic sums of irrational rotations, and recent numerical evidence that it might possess non-trivial q-Gaussian statistics. Using both classical and recent results, we show that the phase average of the sum of centered positions of an orbit, for long times and after normalization, obeys the Cauchy distribution (a q-Gaussian with q=2), while for almost all individual orbits such a sum does not obey any distribution at all. We discuss the question of existence of distributions for KAM tori.
