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Turnability characteristics of solutions of differential systems

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Abstract

For each solution of a differential system, we define a set of turnability exponents of various ranks, which are obtained by minimization and time averaging of the number of zeros and various projections of the angular velocity of the solution onto subspaces of fixed dimensions. We obtain a number of properties of the introduced exponents and relations between them. We show that, in the case of an autonomous system, they are closely related to the absolute values of the imaginary parts of eigenvalues of the operator of the system.

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Authors and Affiliations

  1. 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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Original Russian Text © I.N. Sergeev, 2014, published in Differentsial’nye Uravneniya, 2014, Vol. 50, No. 10, pp. 1353–1361.

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Sergeev, I.N. Turnability characteristics of solutions of differential systems. Diff Equat 50, 1342–1351 (2014). https://doi.org/10.1134/S0012266114100085

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  • DOI: https://doi.org/10.1134/S0012266114100085

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