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Russia Maikop
Section Mathematics
Title Properties of exponents of oscillation of linear autonomous differential system solutions
Author(-s) Stash A.Kh.a
Affiliations Adyghe State Universitya
Abstract In this paper, we study various types of exponents of oscillation (upper or lower, strong or weak) of zeros, roots, hyperroots, strict and non-strict signs of non-zero solutions of linear homogeneous autonomous differential systems on the positive semi-axis. On the set of non-zero solutions of autonomous systems the relations between these exponents of oscillation are established. The spectra of the exponents of autonomous systems' oscillation are fully studied. It turned out that they directly depend on the roots of the corresponding characteristic polynomial of the system. As a consequence, spectra of all exponents of oscillation of autonomous systems with symmetric matrix are found. It is proved that they consist of a single zero value. In addition, a full description of the main values of the exponents of oscillation of such systems is given. These values for the exponents of oscillation of non-strict signs, roots and hyperroots coincided with the set of modules of imaginary parts of the system matrix's eigenvalues, and the exponents of oscillation of strict signs can consist of zero and the least, in absolute magnitude, imaginary part of the complex roots of the corresponding characteristic polynomial.
Keywords differential equations, linear systems, oscillation, number of zeros, exponents of oscillation, Lyapunov exponents
UDC 517.926
MSC 34C10
DOI 10.20537/vm190407
Received 20 August 2019
Language Russian
Citation Stash A.Kh. Properties of exponents of oscillation of linear autonomous differential system solutions, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2019, vol. 29, issue 4, pp. 558-568.
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