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A four-dimensional solvable system of difference equations in the complex domain

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

It is shown that the following class of four-dimensional systems of difference equations of interest

$$\begin{aligned} x_{n+1}&=\frac{a_1}{x_ny_nz_n}+\frac{b_1}{y_nz_nu_n}+\frac{c_1}{z_nu_nx_n}+\frac{d_1}{u_nx_ny_n}\\ y_{n+1}&=\frac{a_2}{x_ny_nz_n}+\frac{b_2}{y_nz_nu_n}+\frac{c_2}{z_nu_nx_n}+\frac{d_2}{u_nx_ny_n}\\ z_{n+1}&=\frac{a_3}{x_ny_nz_n}+\frac{b_3}{y_nz_nu_n}+\frac{c_3}{z_nu_nx_n}+\frac{d_3}{u_nx_ny_n}\\ u_{n+1}&=\frac{a_4}{x_ny_nz_n}+\frac{b_4}{y_nz_nu_n}+\frac{c_4}{z_nu_nx_n}+\frac{d_4}{u_nx_ny_n},\\ \end{aligned}$$

\(n\in {\mathbb N}_0,\) where \(a_i, b_i, c_i, d_i\), \(i=\overline{1,4}\), \(x_0,y_0,z_0,u_0\) are complex numbers, is solvable in closed form, by describing the procedure for solving it in all the cases.

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Authors and Affiliations

  1. Mathematical Institute of the Serbian Academy of Sciences, Knez Mihailova 36/III, 11000, Beograd, Serbia

    Stevo Stević

  2. Operator Theory and Applications Research Group, Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Stevo Stević

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  1. Stevo Stević
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Correspondence to Stevo Stević.

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Stević, S. A four-dimensional solvable system of difference equations in the complex domain. RACSAM 112, 1265–1280 (2018). https://doi.org/10.1007/s13398-017-0421-8

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  • DOI: https://doi.org/10.1007/s13398-017-0421-8

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