Further Dense Properties of the Space of Circle Diffeomorphisms with a Liouville Rotation Number.

In continuation of Matsumoto’s paper (Nonlinearity 25:1495-1511, <xref>2012</xref>) we show that various subspaces are C∞<inline-graphic></inline-graphic>-dense in the space of orientation-preserving C∞<inline-graphic></inline-graphic>-diffeomorphisms of the circle with rotation number α<inline-graphic></inline-graphic>, where α∈S1<inline-graphic></inline-graphic> is any prescribed Liouville number. In particular, for every odometer O<inline-graphic></inline-graphic> of product type we prove the denseness of the subspace of diffeomorphisms which are orbit-equivalent to O<inline-graphic></inline-graphic>. [ABSTRACT FROM AUTHOR]