The Markov Spectra for Triangle Groups

AbstractApplying the Klein modelD2 of the hyperbolic plain and identifying the geodesics inD2 with their poles in the projective plane, the author has developed a method for determining infinite binary trees in the Markov spectrum for a Fuchsian group. In the present paper this method is applied to the groups generated by reflections in the sides of a rectangular triangle in the hyperbolic plane. The complete description of the discrete part of the Markov spectrum for any Hecke group is given