Open Access
February 2015 On manifolds supporting distributionally uniquely ergodic diffeomorphisms
Artur Avila, Bassam Fayad, Alejandro Kocsard
J. Differential Geom. 99(2): 191-213 (February 2015). DOI: 10.4310/jdg/1421415561


A smooth diffeomorphism is said to be distributionally uniquely ergodic (DUE for short) when it is uniquely ergodic and its unique invariant probability measure is the only invariant distribution (up to multiplication by a constant). Ergodic translations on tori are classical examples of DUE diffeomorphisms. In this article we construct DUE diffeomorphisms supported on closed manifolds different from tori, providing some counterexamples to a conjecture proposed by Forni in “On the Greenfield-Wallach and Katok conjectures in dimension three,” Contemporary Mathematics 469 (2008).


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Artur Avila. Bassam Fayad. Alejandro Kocsard. "On manifolds supporting distributionally uniquely ergodic diffeomorphisms." J. Differential Geom. 99 (2) 191 - 213, February 2015.


Published: February 2015
First available in Project Euclid: 16 January 2015

zbMATH: 1316.37015
MathSciNet: MR3302038
Digital Object Identifier: 10.4310/jdg/1421415561

Rights: Copyright © 2015 Lehigh University

Vol.99 • No. 2 • February 2015
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