On the classes of Lipschitz and smooth conjugacies of unimodal maps
Volume 183 / 2004
Fundamenta Mathematicae 183 (2004), 215-227
MSC: Primary 37C15.
DOI: 10.4064/fm183-3-2
Abstract
Under very mild assumptions, any Lipschitz continuous conjugacy between the closures of the postcritical sets of two $C^1$-unimodal maps has a derivative at the critical point, and also on a dense set of its preimages. In a more restrictive situation of infinitely renormalizable maps of bounded combinatorial type the Lipschitz condition automatically implies the $C^1$-smoothness of the conjugacy. Here the critical degree can be any real number $\alpha >1$.
