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RESEARCH PRODUCT
Analytic Exact Upper Bound for the Lyapunov Dimension of the Shimizu–Morioka System
Nikolay KuznetsovGennady A. LeonovT.a. Alexeevasubject
Lyapunov functionPure mathematicsMathematics::Dynamical SystemsGeneral Physics and Astronomylcsh:AstrophysicsLyapunov exponentUpper and lower boundssymbols.namesakeShimizu-Morioka systemDimension (vector space)Attractorlcsh:QB460-466Lyapunov equationLyapunov redesignlcsh:ScienceMathematicsta111Mathematical analysisShimizu–Morioka systemlcsh:QC1-999Nonlinear Sciences::Chaotic DynamicssymbolsLyapunov dimensionlcsh:QDiffeomorphismLyapunov exponentlcsh:Physicsdescription
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. peerReviewed
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-07-22 | Entropy |