Constructing pseudo-Anosov maps with given dilatations
  In this paper, we give sufficient conditions for a Perron number, given as the leading eigenvalue of an aperiodic matrix, to be a pseudo-Anosov dilatation of a compact surface. We give an explicit construction of the surface and the map when the sufficient condition is met. 
Hyungryul Baik, Ahmad Rafiqi, Chenxi Wu
math.GT math.DS