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| Let $f:\mathbb{A}^n\rightarrow\mathbb{A}$ be a rational function. We state the general problem of describing the set of initial conditions $(x_{-n+1},\ldots,x_0)\in\mathbb{A}^n$ such that the iteration $x_{k+1}=f(x_{k-n+1},\ldots,x_k)$ is not well defined for some $k\geq 0$. When $n=1$ and $\mathbb{A}=\mathbb{R},\mathbb{C}$, in some cases it is possible to define a bijection between the forbidden set of the difference equation and a set of symbols. Some topological corollaries and numerical estimates derive from the previous remark. |
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