The Definition of the Indices of Oscillation, Rotation, and Wandering of Nonlinear Differential Systems

The definitions of the indices of oscillation, rotation and wandering, similar to the Lyapunov exponents and suitable for nonlinear systems are given. Definitions are valid even when solutions are not defined on the entire positive time semiaxis. The coincidence of the new indices with those previou...

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Bibliographic Details
Published inMoscow University mathematics bulletin Vol. 76; no. 3; pp. 129 - 134
Main Author Sergeev, I. N.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.05.2021
Springer Nature B.V
Subjects
Analysis
Liapunov exponents
Mathematics
Mathematics and Statistics
Nonlinear systems
Rotation
Lyapunov exponents
rotation
characteristic frequencies
oscillation
differential system
nonlinear system
wandering
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Summary:The definitions of the indices of oscillation, rotation and wandering, similar to the Lyapunov exponents and suitable for nonlinear systems are given. Definitions are valid even when solutions are not defined on the entire positive time semiaxis. The coincidence of the new indices with those previously known in the case of a linear system is established. Various relationships between these indices have been studied.
ISSN:0027-1322
1934-8444
DOI:10.3103/S0027132221030074