Nearly Euclidean Thurston maps
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- by J. W. Cannon, W. J. Floyd, W. R. Parry and K. M. Pilgrim
- Conform. Geom. Dyn. 16 (2012), 209-255
- DOI: https://doi.org/10.1090/S1088-4173-2012-00248-2
- 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.References
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Bibliographic 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
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Conform. Geom. Dyn. 16 (2012), 209-255
- MSC (2010): Primary 37F10, 37F20
- DOI: https://doi.org/10.1090/S1088-4173-2012-00248-2
- MathSciNet review: 2958932