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Some invariants for \(k\)th-order Lyness equation. (English) Zbl 1070.39026

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.

MSC:

39A20 Multiplicative and other generalized difference equations
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References:

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