Journal of Differential Geometry

On manifolds supporting distributionally uniquely ergodic diffeomorphisms

Artur Avila, Bassam Fayad, and Alejandro Kocsard

Full-text: Open access

Abstract

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).

Article information

Source
J. Differential Geom., Volume 99, Number 2 (2015), 191-213.

Dates
First available in Project Euclid: 16 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1421415561

Digital Object Identifier
doi:10.4310/jdg/1421415561

Mathematical Reviews number (MathSciNet)
MR3302038

Zentralblatt MATH identifier
1316.37015

Citation

Avila, Artur; Fayad, Bassam; Kocsard, Alejandro. On manifolds supporting distributionally uniquely ergodic diffeomorphisms. J. Differential Geom. 99 (2015), no. 2, 191--213. doi:10.4310/jdg/1421415561. https://projecteuclid.org/euclid.jdg/1421415561


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