Geodesic
The complete set of relations between the oscillation, rotation and wandering indicators of~solutions of differential systems
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 46 (2015) no. 2, pp. 171-183.

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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, wandering, indicators of solutions, Lyapunov exponents.
Mots-clés : oscillation, rotation 
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I. N. Sergeev. The complete set of relations between the oscillation, rotation and wandering indicators of~solutions of differential systems. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 46 (2015) no. 2, pp. 171-183. http://geodesic.mathdoc.fr/item/IIMI_2015_46_2_a22/

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[2] Sergeev I. N., “Definition and properties of characteristic frequencies of a linear equation”, Journal of Mathematical Sciences, 135:1 (2006), 2764–2793 | DOI | MR | Zbl

[3] Sergeev I. N., “Oscillation and wandering of solutions to a second order differential equation”, Moscow University Mathematics Bulletin, 66:6 (2011), 250–254 | DOI | MR | MR | Zbl

[4] Sergeev I. N., “Oscillation and wandering characteristics of solutions of a linear differential system”, Izvestiya: Mathematics, 76:1 (2012), 141–164 | DOI | DOI | MR | Zbl

[5] Sergeev I. N., “Properties of characteristic frequencies of linear equations of arbitrary order”, Journal of Mathematical Sciences, 197:3 (2014), 410–426 | DOI | DOI | MR | MR | Zbl | Zbl

[6] Sergeev I. N., “The remarkable agreement between the oscillation and wandering characteristics of solutions of differential systems”, Sbornik: Mathematics, 204:1 (2013), 114–132 | DOI | MR | Zbl

[7] Sergeev I. N., “Turnability characteristics of solutions of differential systems”, Differential Equations, 50:10 (2014), 1342–1351 | DOI | DOI | MR | Zbl