Sets of nondifferentiability for conjugacies between expanding interval maps

Thomas Jordan, et al. "Sets of nondifferentiability for conjugacies between expanding interval maps." Fundamenta Mathematicae 206.1 (2009): 161-183. <http://eudml.org/doc/283195>.

@article{ThomasJordan2009,
abstract = {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.},
author = {Thomas Jordan, Marc Kesseböhmer, Mark Pollicott, Bernd O. Stratmann},
journal = {Fundamenta Mathematicae},
keywords = {interval maps; conjugacies; rigidity; sets of nondifferentiability},
language = {eng},
number = {1},
pages = {161-183},
title = {Sets of nondifferentiability for conjugacies between expanding interval maps},
url = {http://eudml.org/doc/283195},
volume = {206},
year = {2009},
}

TY - JOUR
AU - Thomas Jordan
AU - Marc Kesseböhmer
AU - Mark Pollicott
AU - Bernd O. Stratmann
TI - Sets of nondifferentiability for conjugacies between expanding interval maps
JO - Fundamenta Mathematicae
PY - 2009
VL - 206
IS - 1
SP - 161
EP - 183
AB - 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.
LA - eng
KW - interval maps; conjugacies; rigidity; sets of nondifferentiability
UR - http://eudml.org/doc/283195
ER -