Journal of Mathematical Sciences

, Volume 230, Issue 5, pp 770–774 | Cite as

Oscillation, Rotation, and Wandering of Solutions to Linear Differential Systems

  • I. N. Sergeev


For solutions of a linear system on the semi-axis, we introduce a series of Lyapunov exponents that describe the oscillation, rotation, and wandering properties of these solutions. In the case of systems with constant matrices, these exponents are closely related to the imaginary parts of the eigenvalues. We examine the problem on the existence of a similar relationship in the case of piecewise constant of arbitrary systems.

Keywords and phrases

differential equation linear system autonomous system zeros of solution oscillation rotation wandering characteristic exponent 

AMS Subject Classification

34C10, 34D08 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.M. V. Lomonosov Moscow State UniversityMoscowRussia

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