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
DOI:
https://doi.org/10.1090/S1088-4173-2012-00248-2
Published electronically:
August 15, 2012
MathSciNet review:
2958932
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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
MR Author ID:
67750
Email:
floyd@math.vt.edu
W. R. Parry
Affiliation:
Department of Mathematics, Eastern Michigan University, Ypsilanti, Michigan 48197
MR Author ID:
136390
Email:
walter.parry@emich.edu
K. M. Pilgrim
Affiliation:
Department of Mathematics, Indiana University, Bloomington, Indiana 47405
MR Author ID:
614176
Email:
pilgrim@indiana.edu
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.
