Sets of nondifferentiability for conjugacies between expanding interval maps

TM Jordan, M Kesseboehmer, M Pollicott, B Stratmann

Research output: Contribution to journalArticle (Academic Journal)peer-review

9 Citations (Scopus)

Abstract

We study differentiability of topological conjugacies between expanding piecewise C1+ϵ interval maps. If these conjugacies are not C1, then their derivative vanishes Lebesgue almost everywhere. We show that in this case the Hausdorff dimension of the set of points for which the derivative of the conjugacy does not exist lies strictly between zero and one. Moreover, by employing the thermodynamic formalism, we show that this Hausdorff dimension can be determined explicitly in terms of the Lyapunov spectrum. These results then give rise to a “rigidity dichotomy” for the type of conjugacies under consideration.
Translated title of the contributionSets of nondifferentiability for conjugacies between expanding interval maps
Original languageEnglish
Pages (from-to)161 - 183
Number of pages19
JournalFundamenta Mathematicae
Volume206
DOIs
Publication statusPublished - Jan 2009

Bibliographical note

Publisher: Institute of Mathematics Polish Academy of Sciences

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