  Let n be bigger than 1 and let A be an element in the Higman-Thompson group
V_n. We study the structure of the centralizer of a in V_n through a careful
analysis of the action of the group generated by A on the Cantor set C. We make
use of revealing tree pairs as developed by Brin and Salazar from which we
derive discrete train tracks to assist us in our analysis. A consequence of our
structure theorem is that centralizers are finitely generated. Along the way we
give a short argument using revealing tree pairs which shows that cyclic groups
are undistorted in V_n.
