Constructing subdivision rules from rational maps
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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^n is the subdivision map of a finite subdivision rule.Keywords
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This publication has 4 references indexed in Scilit:
- Canonical Thurston ObstructionsAdvances in Mathematics, 2001
- Recognizing constant curvature discrete groups in dimension 3Transactions of the American Mathematical Society, 1998
- A proof of Thurston's topological characterization of rational functionsActa Mathematica, 1993
- Quasiconformal Homeomorphisms and Dynamics I. Solution of the Fatou-Julia Problem on Wandering DomainsAnnals of Mathematics, 1985