On NET maps: Examples and nonexistence results

Saenz, Edgar

doi:10.1090/ecgd/339

On NET maps: Examples and nonexistence results
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by Edgar A. Saenz

Conform. Geom. Dyn. 23 (2019), 147-163

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.

References

B. Bielefeld, Y. Fisher, and J. Hubbard, The classification of preperiodic polynomials as dynamical systems, Journal of the American Mathematical Society, Vol. 5, No. 4, October 1992.
Xavier Buff, Adam Epstein, Sarah Koch, and Kevin Pilgrim, On Thurston’s pullback map, Complex dynamics, A K Peters, Wellesley, MA, 2009, pp. 561–583. MR 2508269, DOI 10.1201/b10617-20
Mario Bonk and Daniel Meyer, Expanding Thurston maps, Mathematical Surveys and Monographs, vol. 225, American Mathematical Society, Providence, RI, 2017. MR 3727134, DOI 10.1090/surv/225
J. W. Cannon, W. J. Floyd, W. R. Parry, and K. M. Pilgrim, Nearly Euclidean Thurston maps, Conform. Geom. Dyn. 16 (2012), 209–255 (electronic).
A. Douady and J. H. Hubbard, A proof of Thurston’s topological characterization of rational functions, Acta Math. 171 (1993), 263–297.
William Floyd, Gregory Kelsey, Sarah Koch, Russell Lodge, Walter Parry, Kevin M. Pilgrim, and Edgar Saenz, Origami, affine maps, and complex dynamics, Arnold Math. J. 3 (2017), no. 3, 365–395. MR 3692494, DOI 10.1007/s40598-017-0071-0
S. Koch, Teichmüller Theory and critically finite endomorphisms, Advances in Mathematics, vol. 248, 2013.
E. A. Saenz, On Nearly Euclidean Thurston maps, Ph.D. Thesis, Virginia Tech, 2012.