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Asymptotic equivalence of difference equations. (English) Zbl 0942.39001
By means of the contraction mapping principle, an asymptotic equivalence is studied between the solutions of a finite-dimensional linear difference equation $$y(n+1)=A(n)y(n)$$ and its nonlinear perturbation $$x({n+1})=A(n)x(n)+F\bigl (n,x(n),Tx(n)\bigr)$$. Under certain conditions on these equations, a homeomorphism is shown between the sets of bounded solutions of the above equations.

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