Sets of nondifferentiability for conjugacies between expanding interval maps

• Autorzy: Thomas Jordan , Marc Kesseböhmer , Mark Pollicott , Bernd O. Stratmann
• Języki publikacji: EN

Abstrakty

EN

We study differentiability of topological conjugacies between expanding piecewise $C^{1+ϵ}$ 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.

Kategorie tematyczne

• 37A10: One-parameter continuous families of measure-preserving transformations
• 37C45: Dimension theory of dynamical systems
• 28A80: Fractals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2009
• Tom: 206
• Numer: 1
• Strony: 161-183

Daty

wydano

2009

Twórcy

autor

Thomas Jordan

• Department of Mathematics, University of Bristol, Bristol, BS8 1TW, UK

autor

Marc Kesseböhmer

• Fachbereich 3-Mathematik und Informatik, Universität Bremen, D-28359 Bremen, Germany

autor

Mark Pollicott

• Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK

autor

Bernd O. Stratmann

• Mathematics Institute, University of St Andrews, St Andrews, KY16 9SS, Scotland

Identyfikatory

DOI

10.4064/fm206-0-10