Orbit equivalence types of circle diffeomorphisms with a Liouville rotation number

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 $\alpha$, it is shown that each of the subspace formed by type ${\mathrm{II}}_1$, ${\mathrm{II}}_{\infty }$, ${\mathrm{III}}_{\lambda }$ ($\lambda >1$), ${\mathrm{III}}_{\infty }$ and ${\mathrm{III}}_0$ diffeomorphisms are $C^{\infty }$-dense in the space of the orientation preserving $C^{\infty }$ diffeomorphisms with rotation number $\alpha$.

14 pages, 2 figures

References in corpus (1)

• Dense properties of the space of the circle diffeomorphisms with a Liouville rotation number

Cited by in corpus (1)

• Modular spectral triples and deformed Fredholm modules