Skip to main content
Log in

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

Ukrainian Mathematical Journal Aims and scope

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

    Google Scholar 

  2. A. M. Samoilenko and Yu. V. Teplinskii,On the Reducibility of Differential Systems in the Space of Bounded Number Sequences [in Russian], Preprint No. 89.44, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1989).

    Google Scholar 

  3. M. G. Filippov, “On the reducibility of systems of differential equations with almost periodic perturbations given on an infinite-dimensional torus,”Dokl. Akad. Nauk Ukr.SSR, SerA, No. 3, 30–33 (1990).

    Google Scholar 

  4. D. I. Martynyuk and N. A. Perestyuk, “On the reducibility of difference equations on a torus,”Vych. Prikl. Mat.,26, 42–48 (1975).

    Google Scholar 

  5. Yu. A. Mitropol'skii, A. M. Samoilenko, and D. I. Martynyuk,Systems of Evolution Equations with Periodic and Quasiperiodic Coefficients [in Russian], Naukova Dumka, Kiev (1984);English translation: Kluwer AP, Dordrecht-Boston-London (1993).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

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

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01059424

Keywords

Navigation