If $V\subset(\mathbb{C}^{*})^{n+1}$ be an algebraic variety. The image $\operatorname{Log}(V)\subset(\mathbb{C}^{*})^{n+1}$ is called the amoeba of $V$, see [4]. Note that amoebas make sense also for varieties over other fields $K$ as long as we have a norm $K^{*}=K\smallsetminus\{0\}\to\mathbb{R}_{+}$. The map $\operatorname{Log}_{K}:(K^{*})^{n+1}\to\mathbb{R}^{n+1}$ is defined by $\operatorname{Log}_{K}(z_{1},\dots,z_{n+1})=(\log||z_{1}||_{K},\dots,\log||z_{n+1}||)$ and the amoeba of $V_{K}\subset(K^{*})^{n+1}$ is defined to be $\operatorname{Log}_{K}(V_{K})$.

A particularly useful case is when $K$ is an algebraically closed field with a non-Archimedian valuation. Recall that a non-Archimedian valuation is a function $\operatorname{val}:K^{*}\to\mathbb{R}$ ²² 2 Sometimes a valuation is defined as minus such a function. such that $\operatorname{val}(a+b)\leq\max\{\operatorname{val}(a),\operatorname{val}(b)\}$ and $\operatorname{val}(ab)=\operatorname{val}(a)+\operatorname{val}(b)$. Note that $e^{\operatorname{val}}$ gives a norm on $K$ and $\operatorname{Log}_{K}$ is nothing but taking the coordinatewise valuation.

Non-Archimedian amoebas of hypersurfaces were completely described in [7]. An example of such field is the field $K$ of the Puiseux series with complex coefficients in $t$. Namely an element of $K$ is a formal series $b(t)=\sum\limits_{k\in J}b_{k}t^{k}$, $b_{k}\in\mathbb{C}^{*}$ where $J\subset\mathbb{R}$ is any bounded from below set contained in a finite union of arithmetic progressions. The valuation is defined by $\operatorname{val}||b(t)||=-\min J$. Note that we used irrational as well as rational powers in the Puiseux series to make the valuation surjective.