Toby HallMASHAEL KUWAYKIB MOSIAR ALDHAFEERI2022-05-262022-05-26https://drepo.sdl.edu.sa/handle/20.500.14154/30905The Dynnikov coordinate system is the fundamental technique for study- ing the action of braids. There are two substantial advantages of the Dynnikov coordinate system: the first one, which will be discussed in this paper, is that it is efficient for solving the word problem in the braid group (deciding the equality of braids); second, it can be used to estimate the growth rate of pseudo-Anosov isotopy classes on the n-times punctured disken