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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

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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:
DateEvent
October 2009Published
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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