On the classes of Lipschitz and smooth conjugacies of unimodal maps

Volume 183 / 2004

Waldemar Pa/luba Fundamenta Mathematicae 183 (2004), 215-227 MSC: Primary 37C15. DOI: 10.4064/fm183-3-2


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 $\alpha >1$.


  • Waldemar Pa/lubaInstitute of Mathematics
    University of Warsaw
    Banacha 2
    02-097 Warszawa, Poland

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