On manifolds supporting distributionally uniquely ergodic diffeomorphisms
Dynamical Systems
2012-11-09 v1 Differential Geometry
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 [For08].
Cite
@article{arxiv.1211.1519,
title = {On manifolds supporting distributionally uniquely ergodic diffeomorphisms},
author = {Artur Avila and Bassam Fayad and Alejandro Kocsard},
journal= {arXiv preprint arXiv:1211.1519},
year = {2012}
}
Comments
20 pages