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 Izv. IMI UdGU, 2015, Issue 2(46), Pages 171–183 (Mi iimi318)

The complete set of relations between the oscillation, rotation and wandering indicators of solutions of differential systems

I. N. Sergeev

Faculty of Mathematics and Mechanics, Lomonosov Moscow State University, Leninskie Gory, 1, Moscow, 119991, Russia

Abstract: In this paper a number of Lyapunov indicators is defined for non-trivial solutions of linear systems on semiaxis to be responsible for their oscillation, rotation and wandering. The indicators are obtained from some functionals of solutions on finite intervals as a result of averaging over time and minimizing for all bases in the phase space. We give a set of relations (equalities or inequalities) between introduced indicators. The set is proved to be full, that is, it cannot be supplemented or strengthened by any meaningful relation.

Keywords: differential equations, linear system, oscillation, rotation, wandering, indicators of solutions, Lyapunov exponents.

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UDC: 517.926
MSC: 34D08

Citation: I. N. Sergeev, “The complete set of relations between the oscillation, rotation and wandering indicators of solutions of differential systems”, Izv. IMI UdGU, 2015, no. 2(46), 171–183

Citation in format AMSBIB
\Bibitem{Ser15} \by I.~N.~Sergeev \paper The complete set of relations between the oscillation, rotation and wandering indicators of~solutions of differential systems \jour Izv. IMI UdGU \yr 2015 \issue 2(46) \pages 171--183 \mathnet{http://mi.mathnet.ru/iimi318} \elib{http://elibrary.ru/item.asp?id=25030044} 

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This publication is cited in the following articles:
1. E. M. Shishlyannikov, “The existence of a two-dimensional bounded system with continual and coinciding spectra of frequencies and of wandering exponents”, Sb. Math., 209:12 (2018), 1812–1826
2. I. N. Sergeev, “Oscillation, rotatability, and wandering characteristic indicators for differential systems determining rotations of plane”, Moscow University Mathematics Bulletin, 74:1 (2019), 20–24
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