Analytic Exact Upper Bound for the Lyapunov Dimension of the Shimizu-Morioka System

被引：9
|
作者：
Leonov, Gennady A. [1 ]
Alexeeva, Tatyana A. [2 ]
Kuznetsov, Nikolay V. [1 ,3 ]
机构：
[1] St Petersburg State Univ, Math & Mech Fac, St Petersburg 198504, Russia
[2] Natl Res Univ, Higher Sch Econ, St Petersburg 190008, Russia
[3] Univ Jyvaskyla, Dept Math Informat Technol, Jyvaskyla 40014, Finland
来源：
ENTROPY | 2015年 / 17卷 / 07期
基金：
俄罗斯科学基金会;
关键词：
Lyapunov exponent; Lyapunov dimension; Shimizu-Morioka system; HAUSDORFF DIMENSION; HIDDEN OSCILLATIONS; ATTRACTORS; ALGORITHMS; INVARIANT; AIZERMAN; LORENZ; TIME;
D O I：
10.3390/e17075101
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
In applied investigations, the invariance of the Lyapunov dimension under a diffeomorphism is often used. However, in the case of irregular linearization, this fact was not strictly considered in the classical works. In the present work, the invariance of the Lyapunov dimension under diffeomorphism is demonstrated in the general case. This fact is used to obtain the analytic exact upper bound of the Lyapunov dimension of an attractor of the Shimizu-Morioka system.
引用
收藏
页码：5101 / 5116
页数：16
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