We study the problem of stability of an invariant toroidal manifold for one class of linear extensions of a dynamical system on a torus. The obtained result is used to investigate the problem of existence of invariant manifold for a nonlinear system of differential equations.
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Translated from Neliniini Kolyvannya, Vol. 19, No. 4, pp. 555–563, October–December, 2016.
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Perestyuk, M.M., Perestyuk, Y.M. On the Stability of Toroidal Manifold for One Class of Dynamical Systems. J Math Sci 228, 314–322 (2018). https://doi.org/10.1007/s10958-017-3623-x
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DOI: https://doi.org/10.1007/s10958-017-3623-x