Some examples of distorted interval diffeomorphisms of intermediate regularity

Abstract

We improve a recent construction of Andrés 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.

15 pages