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

Entropy

Gennady A. Leonov³  Tatyana A. Alexeeva²  Nikolay V. Kuznetsov³  Guanrong Chen¹  C.K. Michael Tse¹  Mustak E. Yalcin¹ 

[1] Mathematics and Mechanics Faculty, St. Petersburg State University, 198504 Peterhof, Saint-Petersburg, Russia; E-Mail;National Research University Higher School of Economics, Soyusa Pechatnikov ul. 16, 190008 Saint-Petersburg, Russia; E-Mail:;Mathematics and Mechanics Faculty, St. Petersburg State University, 198504 Peterhof, Saint-Petersburg, Russia; E-Mail:

关键词: Lyapunov exponent;    Lyapunov dimension;    Shimizu–Morioka system;   

DOI  :  10.3390/e17075101

来源: mdpi

【 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.

【 授权许可】

CC BY   
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