Abstract
We study nontrivial (i.e., containing more than one orbit) minimal sets of the geodesic flow on Γ/T1\Bbb H^2, where Γ 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) Γ is a Schottky group of special kind generated by infinitely many hyperbolic elements, (2) Γ contains a parabolic element (in particular, Γ = PSL(2, \Bbb Z)). This is done by geometric coding of geodesic orbits and constructing a minimal set for symbolic dynamics with infinite alphabet.
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