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Nearly Euclidean Thurston Maps and the Halfspace TheoremKim, Daniel Min 14 November 2016 (has links)
A Thurston map whose postcritical set consists of exactly four points and for which the local degree at each of its critical points is 2 is called textit{nearly Euclidean}. These maps were specified to parse Thurston's combinatorial characterization of rational functions. We determine an extension of the half-space theorem which provides an open hyperbolic half-space such that the negative reciprocal of any fixed slope value is excluded from the boundary of the half-space. / Master of Science
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On Nearly Euclidean Thurston MapsSaenz Maldonado, Edgar Arturo 08 June 2012 (has links)
Nearly 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. / Ph. D.
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