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 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, Engineering and Medicine > 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
Dates:	Date Event October 2009 Published
Volume:	Vol.29
Number:	No.5
Page Range:	pp. 1603-1611
DOI:	10.1017/S0143385708000837
Status:	Peer Reviewed
Access rights to Published version:	Restricted or Subscription Access

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