“…those arising from the family of Japanese continued fractions, named for Hitoshi Nakada, Shunji Ito, and Shigeru Tanaka -see [11,16,24,61] for these systems and some variations. Furthermore, continued fraction algorithms arising from study of geodesic flows on negatively curved surfaces [10,55], and continued fraction expansions over the field of Laurent series [9,46,78,85] would be natural environs to investigate analogues of our results.…”