The Markov Spectra for Triangle Groups Original Research Article

Applying 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.