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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. ISSN 0143-3857

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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
Subjects: Q Science > QA Mathematics
Divisions: Faculty of 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
Volume: Vol.29
Number: No.5
Page Range: pp. 1603-1611
Identification Number: 10.1017/S0143385708000837
Status: Peer Reviewed
Access rights to Published version: Restricted or Subscription Access
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URI: http://wrap.warwick.ac.uk/id/eprint/695

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