Some examples of distorted interval diffeomorphisms of intermediate regularity

Abstract

We improve a recent construction of Andr\'es Navas to produce the first examples of $C^2$-undistorted diffeomorphisms of the interval that are $C^{1+\alpha}$-distorted (for every $\alpha < 1$). We do this via explicit computations due to the failure of an extension to class $C^{1+\alpha}$ of a classical lemma related to the work of Nancy Kopell.