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Entropy 2015, 17(7), 5101-5116; doi:10.3390/e17075101

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

Mathematics and Mechanics Faculty, St. Petersburg State University, 198504 Peterhof, Saint-Petersburg, Russia
National Research University Higher School of Economics, Soyusa Pechatnikov ul. 16, 190008 Saint-Petersburg, Russia
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
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)
View Full-Text   |   Download PDF [3223 KB, uploaded 22 July 2015]   |  


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

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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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.

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