On transversal H\"older regularity for flat Wieler solenoids

Abstract

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.