Finite-dimensional Perron effect of change of all values of characteristic exponents of differential systems |
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Authors: | N A Izobov A V Il’in |
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Institution: | 1. Institute of Mathematics, National Academy of Sciences, Minsk, Belarus 2. Moscow State University, Moscow, Russia
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Abstract: | We obtain a finite-dimensional Perron effect of change of values λ 1 ≤ … ≤ λ n < 0 of all arbitrarily specified negative characteristic exponents of the n-dimensional system of linear approximation with infinitely differentiable bounded coefficients to arbitrarily specified, arranged in ascending order, values β k ≥ λ k , k = 1, …, n, of characteristic exponents of all nontrivial solutions of an n-dimensional nonlinear differential system with an infinitely differentiable perturbation of arbitrary order m > 1 of smallness in a neighborhood of the origin and growth outside it. Each value β k is realized by all nontrivial solutions of the perturbed system issuing from the difference R k |R k?1 of embedded subspaces R 1 ? R 2 ? … ? R n . |
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