Cohomological equations and invariant distributions for minimal circle diffeomorphisms

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.

32 pages. Revised version after referee report. To appear in Duke Mathematical Journal

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