  Thurston and Calegari-Dunfield showed that the fundamental group of some
tautly foliated hyperbolic 3-manifold acts on the circle in a distinctive way
that the action preserves some structure of S^1, so-called a circle lamination.
Indeed, a large class of Kleinian groups acts on the circle preserving a circle
lamination. In this paper, we are concerned with the converse problem that a
group acting on the circle with at least two invariant circle laminations is
Kleinian. We prove that a subgroup of the orientation preserving circle
homeomorphism group is a Fuchsian group whose quotient orbifold is not a
geometric pair of pants (or turnover) if and only if it preserves three circle
laminations with a certain transversality. This is the complete generalization
of the previous result of the first author which is proven under the assumption
that the subgroup is discrete and torsion-free. On the way to our main result,
we also show a structure theorem (generalized pants decomposition) for complete
2-dimensional hyperbolic orbifolds, including the case of infinite type, which
is of independent interest.
