Finite-dimensional Perron effect of change of all values of characteristic exponents of differential systemsстатья
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Аннотация: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 .