当前位置: X-MOL 学术J. Stat. Phys. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Sampling Hyperspheres via Extreme Value Theory: Implications for Measuring Attractor Dimensions
Journal of Statistical Physics ( IF 1.6 ) Pub Date : 2020-06-01 , DOI: 10.1007/s10955-020-02573-5
Flavio Maria Emanuele Pons , Gabriele Messori , M. Carmen Alvarez-Castro , Davide Faranda

The attractor Hausdorff dimension is an important quantity bridging information theory and dynamical systems, as it is related to the number of effective degrees of freedom of the underlying dynamical system. By using the link between extreme value theory and Poincaré recurrences, it is possible to estimate this quantity from time series of high-dimensional systems without embedding the data. In general $$d \le n$$ d ≤ n , where n is the dimension of the full phase-space, as the dynamics freezes some of the available degrees of freedom. This is equivalent to constraining trajectories on a compact object in phase space, namely the attractor. Information theory shows that the equality $$d=n$$ d = n holds for random systems. However, applying extreme value theory, we show that this result cannot be recovered and that $$d

中文翻译:

通过极值理论对超球面进行采样:测量吸引子尺寸的含义

吸引子 Hausdorff 维是连接信息论和动力系统的重要量,因为它与基础动力系统的有效自由度数有关。通过使用极值理论和庞加莱回归之间的联系,可以在不嵌入数据的情况下从高维系统的时间序列中估计这个量。通常 $$d \le n$$ d ≤ n ,其中 n 是完整相空间的维度,因为动力学冻结了一些可用的自由度。这相当于在相空间中的紧凑物体上约束轨迹,即吸引子。信息论表明,等式 $$d=n$$ d = n 对随机系统成立。然而,应用极值理论,我们表明这个结果无法恢复,并且 $$d
更新日期:2020-06-01
down
wechat
bug