FUNDAMENTAL LIMITATIONS FOR ESTIMATING DIMENSIONS AND LYAPUNOV EXPONENTS IN DYNAMIC-SYSTEMS

被引：557

作者：

ECKMANN, JP ^{[1
]}

RUELLE, D ^{[1
]}

机构：

[1] UNIV GENEVA,DEPT PHYS THEOR,CH-1211 GENEVA 4,SWITZERLAND

来源：

PHYSICA D | 1992年 / 56卷 / 2-3期

关键词：

D O I：

10.1016/0167-2789(92)90023-G

中图分类号：

O29 [应用数学];

学科分类号：

070104 [应用数学];

摘要：

We show that values of the correlation dimension estimated over a decade from the Grassberger-Procaccia algorithm cannot exceed the value 2 log10 N if N is the number of points in the time series. When this bound is saturated it is thus not legitimate to conclude that low dimensional dynamics is present. The estimation of Lyapunov exponents is also discussed.

引用

页码：185 / 187

页数：3

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