On the recursive sequence \(x_{n+1}=\alpha-(x_n/x_{n-1})\)
It is shown that for arbitrary real \(\alpha\) the equation in the title has a monotone solution converging to the equilibrium \(\alpha-1\). Under additional assumptions, the equilibrium is globally asymptotically stable and a global attractor. The authors also give conditions such that all solutions are bounded, all solutions are chaotic, resp. such that there exists a 2-periodic solution.
scientific article; zbMATH DE number 2143261