The Mañé–Conze–Guivarc'h lemma for intermittent maps of the circle
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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Official URL: http://dx.doi.org/10.1017/S0143385708000837
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|
|Official Date:||October 2009|
|Page Range:||pp. 1603-1611|
|Access rights to Published version:||Restricted or Subscription Access|
 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.
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