Analytic Exact Upper Bound for the Lyapunov Dimension of the Shimizu–Morioka System
Leonov, G. A., Alexeeva, T. A., & Kuznetsov, N. (2015). Analytic Exact Upper Bound for the Lyapunov Dimension of the Shimizu–Morioka System. Entropy, 17(7), 5101-5116. https://doi.org/10.3390/e17075101
© 2015 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/4.0/).
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.
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Except where otherwise noted, this item's license is described as © 2015 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/4.0/).
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