Next Article in Journal
An Entropy-Based Approach to Path Analysis of Structural Generalized Linear Models: A Basic Idea
Next Article in Special Issue
Generalized Combination Complex Synchronization for Fractional-Order Chaotic Complex Systems
Previous Article in Journal
Averaged Extended Tree Augmented Naive Classifier
Previous Article in Special Issue
A Colour Image Encryption Scheme Using Permutation-Substitution Based on Chaos
Open AccessArticle

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

1
Mathematics and Mechanics Faculty, St. Petersburg State University, 198504 Peterhof, Saint-Petersburg, Russia
2
National Research University Higher School of Economics, Soyusa Pechatnikov ul. 16, 190008 Saint-Petersburg, Russia
3
Department of Mathematical Information Technology, University of Jyväskylä, 40014 Jyväskylä, Finland
*
Author to whom correspondence should be addressed.
Academic Editors: Guanrong Chen, C.K. Michael Tse, Mustak E. Yalcin and Hai Yu
Entropy 2015, 17(7), 5101-5116; https://doi.org/10.3390/e17075101
Received: 26 May 2015 / Revised: 15 July 2015 / Accepted: 17 July 2015 / Published: 22 July 2015
(This article belongs to the Special Issue Recent Advances in Chaos Theory and Complex Networks)
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. View Full-Text
Keywords: Lyapunov exponent; Lyapunov dimension; Shimizu–Morioka system Lyapunov exponent; Lyapunov dimension; Shimizu–Morioka system
MDPI and ACS Style

Leonov, G.A.; Alexeeva, T.A.; Kuznetsov, N.V. Analytic Exact Upper Bound for the Lyapunov Dimension of the Shimizu–Morioka System. Entropy 2015, 17, 5101-5116.

Show more citation formats Show less citations formats

Article Access Map by Country/Region

1
Only visits after 24 November 2015 are recorded.
Back to TopTop