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

 

Nearly Euclidean Thurston maps


Authors: J. W. Cannon, W. J. Floyd, W. R. Parry and K. M. Pilgrim
Journal: Conform. Geom. Dyn. 16 (2012), 209-255
MSC (2010): Primary 37F10, 37F20
Published electronically: August 15, 2012
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Abstract: We take an in-depth look at Thurston's combinatorial characterization of rational functions for a particular class of maps we call nearly Euclidean Thurston maps. These are orientation-preserving branched maps $ f\colon S^2\to S^2$ whose local degree at every critical point is $ 2$ and which have exactly four postcritical points. These maps are simple enough to be tractable, but are complicated enough to have interesting dynamics.


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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

K. M. Pilgrim
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: pilgrim@indiana.edu

DOI: http://dx.doi.org/10.1090/S1088-4173-2012-00248-2
PII: S 1088-4173(2012)00248-2
Received by editor(s): April 16, 2012
Published electronically: August 15, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.