  In this paper, we study asymptotic behavior arising in inverse limit spaces
of dendrites. In particular, the inverse limit is constructed with a single
unimodal bonding map, for which points have unique itineraries and the critical
point is periodic. Using symbolic dynamics, sufficient conditions for two rays
in the inverse limit space to have asymptotic parameterizations are given.
Being a topological invariant, the classification of asymptotic
parameterizations would be a useful tool when determining if two spaces are
homeomorphic.
