Constructing subdivision rules from rational maps

J. W. Cannon, W. J. Floyd, W. R. Parry

Published 2007-03-16Version 1

This paper deepens the connections between critically finite rational maps and finite subdivision rules. The main theorem is that if f is a critically finite rational map with no periodic critical points, then for any sufficiently large integer n the iterate f^n is the subdivision map of a finite subdivision rule.