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Sets of nondifferentiability for conjugacies between expanding interval maps
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Jordan, Thomas, Kesseboehmer, Marc, Pollicott, Mark and Stratmann, Bernd O. (2009) Sets of nondifferentiability for conjugacies between expanding interval maps. In: International Conference on Dynamical Systems held in honor of Michal Misurewicz, Polish Acad Sci, Inst Math, Bedlewo, Poland, 2008. Published in: Fundamenta Mathematicae, Vol.206 pp. 161-183. doi:10.4064/fm206-0-10 ISSN 0016-2736.
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Official URL: http://dx.doi.org/10.4064/fm206-0-10
Abstract
We study differentiability of topological conjugacies between expanding piecewise C1+epsilon interval maps. If these conjugacies are not C-1, 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.
Item Type: | Conference Item (Speech) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Fundamenta Mathematicae | ||||
Publisher: | Polska Akademia Nauk | ||||
ISSN: | 0016-2736 | ||||
Official Date: | 2009 | ||||
Dates: |
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Volume: | Vol.206 | ||||
Number of Pages: | 23 | ||||
Page Range: | pp. 161-183 | ||||
DOI: | 10.4064/fm206-0-10 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Conference Paper Type: | Speech | ||||
Title of Event: | International Conference on Dynamical Systems held in honor of Michal Misurewicz | ||||
Type of Event: | Conference | ||||
Location of Event: | Polish Acad Sci, Inst Math, Bedlewo, Poland | ||||
Date(s) of Event: | 2008 |
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