Difference equations on $\mathbb{R}_*^+$, of the form $u_{n+2}=\frac{f(u_{n+1})}{u_n+λ}$, $λ>0$, with applications to perturbations of dynamical systems - Bastien, Guy; Rogalski, Marc (Sarajevo Journal of Mathematics, 2024)
There is classical difference equation on $\mathbb{R}_*^+$ \begin{equation*}\label{premequat} u_{n+2}u_n=f(u_{n+1}), \tag{1} \end{equation*} that is in particular applied to several symmetric special QRT-applications. We study perturbations of this equation (1) by \begin{equation*}\label{deuxequat} u_{n+2}(u_n+λ)=f(u_{n+1}),\hskip 4mm λ>0, \tag{2} \end{equation*} showing general theorems of regarding permanence, convergence or divergence, and attraction of the fixed point. \vspace*{-.6cm}