Some invariants for \(k\)th-order Lyness equation.
Second and third invariants are established for the \(k\)-th order Lyness equation \[ x_{n+1}=\frac{a+x_n+x_{n-1}+\cdots+x_{n-k+2}}{x_{n-k+1}},\quad n=0,1,2,\dots, \] where the parameter \(a\) is an arbitrary positive number. Furthermore, the independence of the second and third invariants are proved.
scientific article; zbMATH DE number 2140802