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 -coboundaries of such a diffeomorphism is closed in if and only if its rotation number is Diophantine.
Citation
Artur Avila. Alejandro Kocsard. "Cohomological equations and invariant distributions for minimal circle diffeomorphisms." Duke Math. J. 158 (3) 501 - 536, 15 June 2011. https://doi.org/10.1215/00127094-1345662
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