  This paper studies various aspects of inverse limits of locally expanding
affine linear maps on flat branched manifolds, which I call flat Wieler
solenoids. Among the aspects studied are different types of cohomologies, the
rates of mixing given by the Ruelle spectrum of the hyperbolic map acting on
this space, and to solutions of the cohomological equation for primitive
substitution subshifts for H\"older functions. The overarching theme is that
considerations of $\alpha$-H\"older regularity on Cantor sets go a long way.
