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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2009 | 206 | 1 | 161-183

## Sets of nondifferentiability for conjugacies between expanding interval maps

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.

161-183

wydano
2009

### Twórcy

autor
• Department of Mathematics, University of Bristol, Bristol, BS8 1TW, UK
autor
• Fachbereich 3-Mathematik und Informatik, Universität Bremen, D-28359 Bremen, Germany
autor
• Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK
autor
• Mathematics Institute, University of St Andrews, St Andrews, KY16 9SS, Scotland