Duke Mathematical Journal

Cohomological equations and invariant distributions for minimal circle diffeomorphisms

Artur Avila and Alejandro Kocsard

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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 $C^\infty$-coboundaries of such a diffeomorphism is closed in $C^\infty(\mathbb{T})$ if and only if its rotation number is Diophantine.

Article information

Source
Duke Math. J. Volume 158, Number 3 (2011), 501-536.

Dates
First available in Project Euclid: 1 June 2011

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1306934361

Digital Object Identifier
doi:10.1215/00127094-1345662

Mathematical Reviews number (MathSciNet)
MR2805066

Zentralblatt MATH identifier
1225.37052

Subjects
Primary: 37E10: Maps of the circle
Secondary: 37C55: Periodic and quasiperiodic flows and diffeomorphisms 46F05: Topological linear spaces of test functions, distributions and ultradistributions [See also 46E10, 46E35]

Citation

Avila, Artur; Kocsard, Alejandro. Cohomological equations and invariant distributions for minimal circle diffeomorphisms. Duke Math. J. 158 (2011), no. 3, 501--536. doi:10.1215/00127094-1345662. http://projecteuclid.org/euclid.dmj/1306934361.


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References

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