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Conformal Geometry and Dynamics

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Constructing subdivision rules from rational maps


Authors: J. W. Cannon, W. J. Floyd and W. R. Parry
Journal: Conform. Geom. Dyn. 11 (2007), 128-136
MSC (2000): Primary 37F10, 52C20; Secondary 57M12
DOI: https://doi.org/10.1090/S1088-4173-07-00167-1
Published electronically: August 14, 2007
MathSciNet review: 2329140
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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^{\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.


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Additional Information

J. W. Cannon
Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
Email: cannon@math.byu.edu

W. J. Floyd
Affiliation: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061
Email: floyd@math.vt.edu

W. R. Parry
Affiliation: Department of Mathematics, Eastern Michigan University, Ypsilanti, Michigan 48197
Email: walter.parry@emich.edu

DOI: https://doi.org/10.1090/S1088-4173-07-00167-1
Keywords: Finite subdivision rule, rational map, conformality
Received by editor(s): March 15, 2007
Published electronically: August 14, 2007
Additional Notes: This work was supported in part by NSF research grants DMS-0104030 and DMS-0203902.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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