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The Mañé-Conze-Guivarch lemma for intermittent maps of the circle

Morris, ID (2009) The Mañé-Conze-Guivarch lemma for intermittent maps of the circle Ergodic Theory and Dynamical Systems, 29 (5). pp. 1603-1611.

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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: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Date : 2009
DOI : 10.1017/S0143385708000837
Depositing User : Symplectic Elements
Date Deposited : 17 May 2017 12:23
Last Modified : 11 Jun 2019 10:10

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