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Reducibility of nonlinear almost periodic systems of difference equations on an infinite-dimensional torus

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Abstract

We establish sufficient conditions for the reducibility of a nonlinear system of difference equationsx(t+1)=x(t)+ω+P(x(t),t+λ to a system y(t+1)= y(t)+ω, wherex, ω, λ∈ m and the infinite-dimensional vector function P(x(t),t) is 2πp-periodic inx i i=1,2,...) and almost periodic int with a frequency basisα.

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References

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    N. N. Bogolyubov, Yu. A. Mitropol'skii, and A. M. Samoilenko,Method of Accelerated Convergence in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev (1969).

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 9, pp. 1216–1223, September, 1994.

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Samoilenko, A.M., Martynyuk, D.I. & Perestyuk, N.A. Reducibility of nonlinear almost periodic systems of difference equations on an infinite-dimensional torus. Ukr Math J 46, 1336–1344 (1994). https://doi.org/10.1007/BF01059424

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Keywords

  • Nonlinear System
  • Difference Equation
  • Vector Function
  • Periodic System