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Two-dimensional anti-Perron effect of changing arbitrary different positive Lyapunov exponents of a linear approximation system to negative ones by higher-order perturbations

EDN: TZHQBX

Abstract

A two-dimensional anti-Perron effect of changing arbitrary different positive Lyapunov exponents of a linear differential system to negative ones by a perturbation of a higher order of smallness is realized.

About the Authors

N. A. Izobov
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus

Minsk



A. V. Il’in
Moscow State University
Russian Federation

Moscow



References

1. Izobov N. A. Linear systems of ordinary differential equations. Mathematical analysis. Results of science and technology, 1974, vol. 12, pp. 71–146 (in Russian).

2. Perron O. Die Stabilita¨tsfrage bei Differentialgleichungen. Math. Zeitschr., 1930, Bd. 32, H. 5, S. 703–728.

3. Leonov G. A. Chaotic Dynamics and Classical Theory of Motion Stability. Izhevsk, Inst. Komp’yut. Issled., 2006.

4. Izobov N. A., Il’in A. V. Existence of an anti-Perron effect of change of positive exponents of the linear approximation system to negative ones under perturbations of a higher order of smallness. Differ. Equat., 2023, vol. 59, no. 12, pp. 1591–1597.

5. Izobov N. A., Il’in A. V. Construction of solutions with negative exponents of a differential system in the two-dimensional anti-Perron effect under higher-order perturbations. Differ. Equat., 2024, vol. 60, no. 12, pp. 1668–1674.

6. Gelbaum B. R., Olmsted J. M. H. Counterexamples in Analysis. San Francisco, Holden-Day, 1964.

7. Izobov N. A., Mazanik S. A. On linear systems asymptotically equivalent under exponentially decaying perturbations. Differ. Equat., 2006, vol. 42, no. 2, pp. 182–187.

8. Izobov N. A., Il’in A. V. Variant of the anti-Perron effect of change of Lyapunov exponents of two-dimensional differential systems under perturbations of a higher order of smallness. Differ. Equat., 2023, vol. 59, no. 8, pp. 1143–1144.


Review

For citations:


Izobov N.A., Il’in A.V. Two-dimensional anti-Perron effect of changing arbitrary different positive Lyapunov exponents of a linear approximation system to negative ones by higher-order perturbations. Proceedings of the Institute of Mathematics of the NAS of Belarus. 2025;33(2):96-102. (In Russ.) EDN: TZHQBX

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ISSN 1812-5093 (Print)