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

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Abstract

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.

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ACKNOWLEDGMENTS

The author is grateful to V.V. Bykov for valuable comments that contributed to a significant improvement of the text of the article.

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Authors and Affiliations

  1. Chair of Differential Equations, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

    I. N. Sergeev

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  1. I. N. Sergeev
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Correspondence to I. N. Sergeev.

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Sergeev, I.N. The Definition of the Indices of Oscillation, Rotation, and Wandering of Nonlinear Differential Systems. Moscow Univ. Math. Bull. 76, 129–134 (2021). https://doi.org/10.3103/S0027132221030074

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  • DOI: https://doi.org/10.3103/S0027132221030074

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