On Noncompact Minimal Sets of the Geodesic Flow

We study nontrivial (i.e., containing more than one orbit) minimal sets of the geodesic flow on \T ¹², where is a nonelementary Fuchsian group. It is not difficult to prove that nontrivial compact minimal sets always exist. We establish the existence of nontrivial noncompact minimal sets in two cases: (1) is a Schottky group of special kind generated by infinitely many hyperbolic elements, (2) contains a parabolic element (in particular, = PSL(2, )). This is done by geometric coding of geodesic orbits and constructing a minimal set for symbolic dynamics with infinite alphabet.