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Conformal Geometry and Dynamics

Published by the American Mathematical Society since 1997, the purpose of this electronic-only journal is to provide a forum for mathematical work in related fields broadly described as conformal geometry and dynamics. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.49.

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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
Published electronically: August 15, 2012


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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Bibliographic Information
  • J. W. Cannon
  • Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
  • Email:
  • W. J. Floyd
  • Affiliation: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061
  • MR Author ID: 67750
  • Email:
  • W. R. Parry
  • Affiliation: Department of Mathematics, Eastern Michigan University, Ypsilanti, Michigan 48197
  • MR Author ID: 136390
  • Email:
  • K. M. Pilgrim
  • Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
  • MR Author ID: 614176
  • Email:
  • 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:
  • MathSciNet review: 2958932