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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. 16031611. ISSN 01433857

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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 

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:  01433857 
Official Date:  October 2009 
Volume:  Vol.29 
Number:  No.5 
Page Range:  pp. 16031611 
Identification Number:  10.1017/S0143385708000837 
Status:  Peer Reviewed 
Access rights to Published version:  Restricted or Subscription Access 
References:  [1] Barabanov, N. E.. On the Lyapunov exponent of discrete inclusions I. Avtomat. i Telemekh. 2 (1988), 40–46; English translation: Autom. Remote Control 49 (1988), 152–157. 
URI:  http://wrap.warwick.ac.uk/id/eprint/695 
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