PURELY PERIODIC ROSEN CONTINUED FRACTIONS

We consider the two Hecke groups G 4 and G 6 generated by the transformations S and T defined by S(z) ( z ) = z +Am m and T ( z ) = - 1 / z where A m = 2 cos (pi/ m ) with m E { 4 , 6}. } . We give a full characterization of purely periodic Rosen continued fractions over G 4 and G 6 . Finally, we end by finding a family of examples of purely periodic Rosen expansions of period length two and some related examples.