Consider the space $X = \{0, 1\}^{\mathbb{Z}}$ and $Y = \{0, 1\}^{\mathbb{N}}$. It is a well known fact that given a potential $V \colon X \to \mathbb{R}$ there exists a potential $v \colon Y \to \mathbb{R}$ that is cohomologous to $V$, i.e., such that $v = V + h \circ \sigma - h$ where $\sigma$ is the shift map (the unilateral shift in Y and the bilateral shift in X).

 Now consider the space $\{0, 1\}^{{\mathbb{Z}}^2}$ and $\{0, 1\}^{{\mathbb{N}}^2}$; in this spaces we can define two shifts, $\sigma_x$ and $\sigma_y$ that corresponds to the horizontal shift and to the vertical shift, and that satisfies $\sigma_x \circ \sigma_y = \sigma_y \circ \sigma_x$. Given a potential $U \colon \{0, 1\}^{{\mathbb{Z}}^2} \to \mathbb{R}$ we are able to show that there exists a potential $ u \colon \{0, 1\}^{{\mathbb{N}}^2} \to \mathbb{R}$ such that $ u = U + g \circ \sigma_x - g + h \circ \sigma_y - h$. 

 This is a joint work with E. Garibaldi (UNICAMP) and E. Artuso (UFRGS), partially supported by CNPq