The space of vertical and horizontal right hyperbolas and the lines tangent to these hyperbolas is considered in the double plane. It is proved that an injective map from the middle region of a considered hyperbola that takes hyperbolas and lines in this space to other hyperbolas and lines in this space must be a direct or indirect linear fractional transformation.
Michael Bolt, Department of Mathematics and Statistics , Calvin College Grand Rapids, MI firstname.lastname@example.org
Hays, James and Mitchell, Todd
"The Most General Planar Transformations that Map Hyperbolas to Hyperbolas,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 10
, Article 6.
Available at: http://scholar.rose-hulman.edu/rhumj/vol10/iss2/6