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Comparing the Spectra of Oscillation Exponents of a Nonlinear System and the First Approximation System

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Abstract

We study the oscillation exponents of differential systems. It is established that there is no dependence between the spectra of oscillation exponents of a nonlinear system and the system of its first approximation; namely, a two-dimensional nonlinear system is constructed such that the spectra of oscillation exponents of its restriction to any open neighborhood of zero on the phase plane consist of all rational numbers in the interval \([0,1] \) and the spectra of the linear system of its first approximation consist of only one element.

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REFERENCES

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ACKNOWLEDGMENTS

The author expresses his sincere gratitude to Prof. I.N. Sergeev for posing the problem and for valuable advice.

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Authors and Affiliations

  1. Adyghe State University, Maikop, 385000, Russia

    A. Kh. Stash

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  1. A. Kh. Stash
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Correspondence to A. Kh. Stash.

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Translated by V. Potapchouck

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Stash, A.K. Comparing the Spectra of Oscillation Exponents of a Nonlinear System and the First Approximation System. Diff Equat 59, 1147–1150 (2023). https://doi.org/10.1134/S0012266123080128

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  • DOI: https://doi.org/10.1134/S0012266123080128

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