Monotonicity of solutions converging to a saddle point equilibrium (Q1876699)

The author considers the initial value problem (*) \(y_{n+1}=f(y_{n-1},y_n)\), \(y_{-1},y_0\in I\), where \(f:I\times I\to I\) is a continuously differentiable function. Sufficient conditions are given which assure that every solution of equation (*) which converges to a saddle point equilibrium of (*) is monotone. This result is then applied to a second order rational difference equation.