Cohomological equations and invariant distributions for minimal circle diffeomorphisms

Details Cohomological equations and invariant distributions for minimal circle diffeomorphisms Cohomological equations and invariant distributions for minimal circle diffeomorphisms

2010-02-17

arxiv.org/abs/1002.3392v2

Mathematics

Dynamical Systems

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

Scientific paper

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.

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