Constructing subdivision rules from rational maps

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

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Bibliographic Details
Published in:Conformal geometry and dynamics 2007-08, Vol.11 (10), p.128-136
Main Authors: Cannon, J., Floyd, W., Parry, W.
Format: Article
Language:English
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Summary:This paper deepens the connections between critically finite rational maps and finite subdivision rules. The main theorem is that if f f is a critically finite rational map with no periodic critical points, then for any sufficiently large integer n n the iterate f ∘ n f^{\circ n} is the subdivision map of a finite subdivision rule. This enables one to give essentially combinatorial models for the dynamics of such iterates.
ISSN:1088-4173
1088-4173
DOI:10.1090/S1088-4173-07-00167-1