Cohomological equations and invariant distributions for minimal circle diffeomorphisms
Dynamical Systems
2019-12-19 v2 Classical Analysis and ODEs
Abstract
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 a consequence of this, we show that the space of real smooth coboundaries of such a diffeomorphism is closed if and only if its rotation number is Diophantine.
Cite
@article{arxiv.1002.3392,
title = {Cohomological equations and invariant distributions for minimal circle diffeomorphisms},
author = {Artur Avila and Alejandro Kocsard},
journal= {arXiv preprint arXiv:1002.3392},
year = {2019}
}
Comments
32 pages. Revised version after referee report. To appear in Duke Mathematical Journal