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arXiv · 1206.3740

Orbit equivalence types of circle diffeomorphisms with a Liouville rotation number

Shigenori Matsumoto
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Abstract

This paper is concerned about the orbit equivalence types of $C^\infty$ diffeomorphisms of $S^1$ seen as nonsingular automorphisms of $(S^1,m)$, where $m$ is the Lebesgue measure. Given any Liouville number $α$, it is shown that each of the subspace formed by type ${\rm II}_1$, ${\rm II}_\infty$, ${\rm III}_λ$ ($λ>1$), ${\rm III}_\infty$ and ${\rm III}_0$ diffeomorphisms are $C^\infty$-dense in the space of the orientation preserving $C^\infty$ diffeomorphisms with rotation number $α$.

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Shigenori Matsumoto. 2012-06-17. Orbit equivalence types of circle diffeomorphisms with a Liouville rotation number. https://doi.org/10.1088/0951-7715%2F26%2F5%2F1401

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