Centralizers of rank-1 homeomorphisms
  We give a definition for a rank-1 homeomorphism of a zero-dimensional Polish space X. We show that if a rank-1 homeomorphism of X satisfies a certain non-degeneracy condition, then it has trivial centralizer in the group of all homeomorphisms of X, i.e., it commutes only with its integral powers. 
Aaron Hill
math.DS math.LO