Residual Subsets in the Space of Finitely Generated Groups of Diffeomorphisms of the Circle

Finitely generated groups of diffeomorphisms of the circle are considered in different problems of geometry, wave theory, variational calculus, etc. In particular, the set of such groups contains groups freely acting on the orbits of almost each point of the circle. The present paper deals with the structure of the set of finitely generated groups of diffeomorphisms with a given number of generators and with the above property. It is shown that such a set contains a residual subset (i.e., contains the countable intersection of open everywhere dense subsets).