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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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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:

0143-3857

Official Date:

October 2009

Dates:

Date	Event
October 2009	Published

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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