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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 ISSN 0143-3857.
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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 T−g+β, where f is a prescribed continuous function, T is a weakly expanding transformation of the circle having an indifferent fixed point, and β is the maximum ergodic average of f. Using a method due to T. Bousch, we show that continuous solutions g always exist when the Hölder exponent of f is close to 1. In the converse direction, we construct explicit examples of continuous functions f with low Hölder exponent for which no continuous solution g exists. We give sharp estimates on the best possible Hölder regularity of a solution g given the Hölder regularity of f.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Ergodic theory, Circle, Geometry, Plane, Lipschitz spaces, Curves, Plane | ||||
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 | ||||
Page Range: | pp. 1603-1611 | ||||
DOI: | 10.1017/S0143385708000837 | ||||
Status: | Peer Reviewed | ||||
Access rights to Published version: | Restricted or Subscription Access |
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