Abstract
We prove the existence of a two-dimensional linear system x˙ = A(t)x, t ≥ t0, withbounded infinitely differentiable coefficients and all positive characteristic exponents, as wellas an infinitely differentiable m-perturbation f(t, y) having an order m 1 of smallness ina neighborhood of the origin y = 0 and an order of growth not exceeding m outside it, such thatthe perturbed system y˙ = A(t)y + f(t, y), y ∈ R2, t ≥ t0, has a solution y(t) with a negativeLyapunov exponent.
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