, Volume 125, Issue 3, pp 487-521

Symbolic dynamics for triangle groups

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We generalize E. Artin’s continued fraction coding of the geodesics on the modular surface to any finite index subgroup Θ of a nonuniform hyperbolic triangle group Γ. D. Mayer’s study of the Selberg zeta function of PSl (2, Z ) is extended to Θ and its group representations. We give representatives for Γ-primitive conjugacy classes and derive a Markov system of interval maps for Γ and a Markov partition for the billiard flow on Γ\ SH 2 . This leads to identities for values of the dilogarithm function at algebraic numbers. We also find the Γ-analogues of Gauss measure on [0,1].

Oblatum 16-VIII-1993 & 15-VIII-1994 & 2-I-1996