# On manifolds supporting distributionally uniquely ergodic diffeomorphisms

@article{Avila2012OnMS,
title={On manifolds supporting distributionally uniquely ergodic diffeomorphisms},
author={Artur Avila and Bassam Fayad and Alejandro Kocsard},
journal={arXiv: Dynamical Systems},
year={2012}
}
• Published 7 November 2012
• Mathematics
• arXiv: Dynamical Systems
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].
7 Citations
• Mathematics
• 2016
We prove that every homogeneous flow on a finite-volume homogeneous manifold has countably many independent invariant distributions unless it is conjugate to a linear flow on a torus. We also prove
• Mathematics
• 2013
We prove that every homogeneous flow on a finite-volume homogeneous manifold has countably many independent invariant distributions unless it is conjugate to a linear flow on a torus. We also prove
• Mathematics
• 2013
We construct examples of volume-preserving uniquely ergodic (and hence minimal) real-analytic diffeomorphisms on odd-dimemsional spheres
We study the linear cohomological equation in the smooth category over quasi-periodic cocycles in T × SU(2). We prove that, under a full measure condition on the rotation in T, for a generic cocycle
We provide a general argument for the failure of Anosov-Katok-like constructions to produce Cohomologically Rigid diffeomorphisms in manifolds other than tori. A $C^{\infty }$ smooth diffeomorphism
We study the linear cohomological equation in the smooth category over quasi-periodic cocycles in $\mathbb{T} ^{d} \times SU(2)$. We prove that, under a full measure condition on the rotation in
AbstractWe continue our study of the local theory for quasiperiodic cocycles in $${\mathbb{T} ^{d} \times G}$$Td×G , where $${G=SU(2)}$$G=SU(2) , over a rotation satisfying a Diophantine condition

## References

SHOWING 1-10 OF 14 REFERENCES

• Mathematics
• 2010
Given any smooth circle diffeomorphism with irrational rotation number, we show that its invariant probability measure is the only invariant distribution (up to multiplication by a real constant). As
• Mathematics
• 2003
There are infinitely many obstructions to existence of smooth solutions of the cohomological equation Uu = f , where U is the vector field generating the horocycle flow on the unit tangent bundle SM
• Mathematics
• 2012
Although invariant measures are a fundamental tool in Dynamical Systems, very little is known about distributions (i.e. linear functionals defined on some space of smooth functions on the underlying
• Mathematics
• 2005
Let X be a vector field on a compact connected manifold M. An important question in dynamical systems is to know when a function g:M -> R is a coboundary for the flow generated by X, i.e. when there
Let G be a connected compact Lie group, and U a connected closed subgroup of it. As is known [1 ], the difference r(G)-r(U) in the ranks is a homotopy invariant of the manifold G/U. When r(G) = r{U),
• Mathematics
• 1989
Preface 1. Elementary theory of nilpotent Lie groups and Lie algebras 2. Kirillov theory 3. Parametrization of coadjoint orbits 4. Plancherel formula and related topics 5. Discrete cocompact
We survey recent progress on the Greenfield-Wallach and Katok conjectures on globally hypoelliptic and cohomology free vector fields and derive a proof of the conjectures in dimension three. The
• Mathematics
• 1990
Preface 1. Elementary theory of nilpotent Lie groups and Lie algebras 2. Kirillov theory 3. Parametrization of coadjoint orbits 4. Plancherel formula and related topics 5. Discrete cocompact
Compact Lie Groups.- Representations.- HarmoniC Analysis.- Lie Algebras.- Abelian Lie Subgroups and Structure.- Roots and Associated Structures.- Highest Weight Theory.
• Physics
• 1977
© Bulletin de la S. M. F., 1977, tous droits réservés. L’accès aux archives de la revue « Bulletin de la S. M. F. » (http://smf. emath.fr/Publications/Bulletin/Presentation.html) implique l’accord