Sets of non-differentiability for conjugacies between expanding interval maps
Dynamical Systems
2010-06-30 v1
Abstract
We study differentiability of topological conjugacies between expanding piecewise interval maps. If these conjugacies are not , then they have zero derivative almost everywhere. We obtain the result 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. Using multifractal analysis and thermodynamic formalism, we show that this Hausdorff dimension is explicitly determined by the Lyapunov spectrum. Moreover, we show that these results give rise to a "rigidity dichotomy" for the type of conjugacies under consideration.
Cite
@article{arxiv.0807.0115,
title = {Sets of non-differentiability for conjugacies between expanding interval maps},
author = {Thomas Jordan and Marc Kesseböhmer and Mark Pollicott and Bernd O. Stratmann},
journal= {arXiv preprint arXiv:0807.0115},
year = {2010}
}