For typical properly ordered and minimal Bratteli diagrams $(B,\leq_r)$, it is shown that there are finitely many invariant distributions $\mathcal{ D}_i$ which are the only obstructions to solving the cohomological equation $f = u-u\circ \phi$ for the corresponding adic transformation $\phi:X_B\rightarrow X_B$ and for $\alpha$-H\"older $f$ with $\alpha$ large enough. These invariant distributions are then used to define cyclic cocycles, a.k.a. traces $\tau:K_0(\mathcal{ A}_\phi)\rightarrow \mathbb{ R}$ for the crossed product algebra $\mathcal{ A}_\phi$.
Categories: math.DS math.OA