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

In continuation of Matsumoto’s paper (Nonlinearity 25:1495–1511, 2012) we show that various subspaces are (C^{infty })-dense in the space of orientation-preserving (C^{infty })-diffeomorphisms of the circle with rotation number (alpha ), where (alpha in {mathbb {S}}^1) is any prescribed Liouville number. In particular, for every odometer ({mathcal {O}}) of product type we prove the denseness of the subspace of diffeomorphisms which are orbit-equivalent to ({mathcal {O}}).