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Conformal Geometry and Dynamics

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On NET maps: Examples and nonexistence results


Author: Edgar A. Saenz
Journal: Conform. Geom. Dyn. 23 (2019), 147-163
MSC (2010): Primary 37F10, 37F20
DOI: https://doi.org/10.1090/ecgd/339
Published electronically: August 21, 2019
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Abstract: A Thurston map is called nearly Euclidean if its local degree at each critical point is 2 and it has exactly four postcritical points. Nearly Euclidean Thurston (NET) maps are simple generalizations of rational Lattès maps. We investigate when such a map has the property that the associated pullback map on Teichmüller space is constant. We also show that no Thurston map of degree 2 has constant pullback map.


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Additional Information

Edgar A. Saenz
Affiliation: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061
Email: easaenzm@math.vt.edu

DOI: https://doi.org/10.1090/ecgd/339
Received by editor(s): July 4, 2015
Received by editor(s) in revised form: August 16, 2018
Published electronically: August 21, 2019
Article copyright: © Copyright 2019 American Mathematical Society