Lattès maps and finite subdivision rules
Authors:
J. W. Cannon, W. J. Floyd and W. R. Parry
Journal:
Conform. Geom. Dyn. 14 (2010), 113140
MSC (2010):
Primary 37F10, 52C20; Secondary 57M12
Published electronically:
April 28, 2010
MathSciNet review:
2629972
Fulltext PDF Free Access
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Additional Information
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 1skeleton 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
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:
http://dx.doi.org/10.1090/S1088417310002031
PII:
S 10884173(10)002031
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.
