Dynnikov Coordinates and ？？？？–Train Tracks

A well known way to coordinatize multicurves on a given surface is to use train tracks. In the case where the surface is the ？？– punctured disk ？？？？ an alternative and efficient way to coordinatize multicurves is achieved by the Dynnikov coordinate system which gives an explicit bijection between the set of multicurves on ？？？？ and ？ 2？？？4 \{0}. In this paper we introduce