Physical Sciences and Mathematics Commons^™

Constructing Subdivision Rules From Rational Maps, J. W. Cannon, W. J. Floyd, W. R. Parry

Faculty Publications

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 is the subdivision map of a finite subdivision rule. This enables one to give essentially combinatorial models for the dynamics of such iterates.