H\"older properties of Weierstrass-like solutions of $\theta$-twisted cohomological equations

Abstract

It is proved that bounded solutions of modified ($\theta$-twisted) cohomological equations for expanding circle maps are $\theta$-H\"{o}lder continuous but are not $(\theta+\gamma)$-H\"{o}lder continuous for every $\gamma>0$ at almost every point. This gives new examples of "nonlinear" Weierstrass-like functions for which the optimal \holder exponent at most points is known.