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

Abstract

Italia S.r.l. It is shown that the following class of four-dimensional systems of difference equations of interest xn+1=a1xnynzn+b1ynznun+c1znunxn+d1unxnynyn+1=a2xnynzn+b2ynznun+c2znunxn+d2unxnynzn+1=a3xnynzn+b3ynznun+c3znunxn+d3unxnynun+1=a4xnynzn+b4ynznun+c4znunxn+d4unxnyn,n∈ N0, where ai, bi, ci, di, i= 1 , 4 ¯ , x0, y0, z0, u0 are complex numbers, is solvable in closed form, by describing the procedure for solving it in all the cases.