Hyperbolic transformations on cubics in H²

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Marfai, Frank S.
Henri Poincaré 1854-1912; Hyperbolic Geometry; Hyperbolic Differential equations; Möbius transformations; Mathematics
thesis / dissertation description
The purpose of this thesis is to study the effects of hyperbolic transformations on the cubic that is determined by locus of centroids of the equilateral triangles in H² whose base coincides with the line y=0, and whose common vertex is at the origin. The derivation of the formulas within this work are based on the Poincaré disk model of H², where H² is understood to mean the hyperbolic plane. The thesis explores the properties of both the untransformed cubic (the original locus of centroids) and the transformed cubic (the original cubic taken under a linear fractional transformation).