An example of a kinematically induced Lie circle transformation of the isotropic plane (Q1281746)

In the isotropic plane there exists a oneparametric motion \(\zeta\) which moves all points on straight lines. The point-paths of straight lines and circles in general have circles as envelopes. Thus, \(\zeta\) induces a circular transformation \(\pi\) in the set of ``generalized isotropic circles'' (containing points, nonisotropic straight lines and isotropic circles). The author is able to show, that \(\pi\) is a Lie-map which is neither a Möbius-map nor a Laguerre-transformation.