## Constructing subdivision rules from rational maps

###
J. W. Cannon, W. J. Floyd, R. Kenyon, and W. R. Parry

March 15, 2007

### Abstract

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
$f^{\circ n}$ is the subdivision map of a finite subdivision rule.
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