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The Mañé-Conze-Guivarc'h lemma for intermittent maps of the circle
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Morris, Ian D. (2009) The Mañé-Conze-Guivarc'h lemma for intermittent maps of the circle. Ergodic Theory and Dynamical Systems, Vol.29 (No.5). pp. 1603-1611. doi:10.1017/S0143385708000837
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Official URL: http://dx.doi.org/10.1017/S0143385708000837
Abstract
We study the existence Of Solutions g to the functional inequality f <= g circle T - g + beta where f is a prescribed continuous function, T is a weakly expanding transformation of the circle having an indifferent fixed point, and beta is the maximum ergodic average of f. Using a method due to T. Bousch, we show that continuous Solutions g always exist when the Holder exponent of f is close to 1. In the converse direction, we construct explicit examples of continuous functions f with low Holder exponent for which no continuous solution g exists. We give sharp estimates oil the best possible Holder regularity of a solution g given the Holder regularity of f.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science > Mathematics | ||||
| Journal or Publication Title: | Ergodic Theory and Dynamical Systems | ||||
| Publisher: | Cambridge University Press | ||||
| ISSN: | 0143-3857 | ||||
| Official Date: | October 2009 | ||||
| Dates: |
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| Volume: | Vol.29 | ||||
| Number: | No.5 | ||||
| Number of Pages: | 9 | ||||
| Page Range: | pp. 1603-1611 | ||||
| DOI: | 10.1017/S0143385708000837 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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