The Most General Planar Transformations That Map Parabolas into Parabolas

@inproceedings{Bolt2008TheMG,
title={The Most General Planar Transformations That Map Parabolas into Parabolas},
author={Michael Bolt and TIMOTHY FERDINANDS and LANDON KAVLIE},
year={2008}
}

Consider the space of vertical parabolas in the plane interpreted generally to include nonvertical lines. It is proved that an injective map from a closed region bounded by one such parabola into the plane that maps vertical parabolas to other vertical parabolas must be the composition of a Laguerre transformation with a non-isotropic dilation. Here, a Laguerre transformation refers to a linear fractional or antilinear fractional transformation of the underlying dual plane.