On the shape and dimension of the Lorenz attractor

被引：38

作者：

Doering, CR ^{[1
]}

Gibbon, JD ^{[1
]}

机构：

[1] UNIV LONDON IMPERIAL COLL SCI & TECHNOL,DEPT MATH,LONDON SW7 2BZ,ENGLAND

来源：

DYNAMICS AND STABILITY OF SYSTEMS | 1995年 / 10卷 / 03期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1080/02681119508806207

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is shown how the global attractor of the Lorenz equations is contained in a volume bounded by a sphere, a cylinder, the volume between two parabolic sheets, an ellipsoid and a cone. The first four are absorbing volumes while the interior of the cone is expelling. By a numerical search over these volumes, it is found that the origin is the most unstable point on the attractor and that an upper bound for the attractor's Lyapunov dimension is 2.401 when b = 8/3, r = 28 and sigma = 10.

引用

页码：255 / 268

页数：14

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