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Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173


Lattès maps and finite subdivision rules

Authors: J. W. Cannon, W. J. Floyd and W. R. Parry
Journal: Conform. Geom. Dyn. 14 (2010), 113-140
MSC (2010): Primary 37F10, 52C20; Secondary 57M12
Published electronically: April 28, 2010
MathSciNet review: 2629972
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Abstract: This paper is concerned with realizing Lattès maps as subdivision maps of finite subdivision rules. The main result is that the Lattès maps in all but finitely many analytic conjugacy classes can be realized as subdivision maps of finite subdivision rules with one tile type. An example is given of a Lattès map which is not the subdivision map of a finite subdivision rule with either (i) two tile types and 1-skeleton of the subdivision complex a circle or (ii) one tile type.

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Additional Information

J. W. Cannon
Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602

W. J. Floyd
Affiliation: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061

W. R. Parry
Affiliation: Department of Mathematics, Eastern Michigan University, Ypsilanti, Michigan 48197

PII: S 1088-4173(10)00203-1
Keywords: Finite subdivision rule, Latt\`es map, rational map, conformality
Received by editor(s): November 6, 2009
Published electronically: April 28, 2010
Additional Notes: We thank Kevin Pilgrim for piquing our interest in realizing Lattès maps as subdivision maps of finite subdivision rules.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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