Saenz Maldonado, Edgar Arturo2014-03-142014-03-142012-05-01etd-05102012-234227http://hdl.handle.net/10919/27637Nearly Euclidean Thurston maps are simple generalizations of rational Lattes maps. A Thurston map is called nearly Euclidean if its local degree at each critical point is 2 and it has exactly four postcritical points. We investigate when such a map has the property that the associated pullback map on Teichmuller space is constant. We also show that no Thurston map of degree 2 has constant pullback map.In Copyrightnonseparating setsconstant pullback mapfinite subdivision rulesThurston mapsDissertationhttp://scholar.lib.vt.edu/theses/available/etd-05102012-234227/