Distribution of the reduced quadratic irrationals arising from the odd continued fraction expansion

This paper investigates the quadratic irrationals that arise as periodic points of Gauss type shift associated to odd continued fraction expansion. It is shown these numbers, which we call O-reduced, when ordered by length closed primitive geodesic on some modular surface Γ∖H, are equidistributed with respect Lebesgue absolutely continuous invariant probability measure Odd shift.