Abstract
For any given cross ratio \(\delta \in \mathbb C\) we define a non-linear Möbius-invariant procedure creating vertices of a new quadrangle from a given quadrangle. Reiterating the process we discover a remarkable regularizing property. The values \(\delta \in \mathbb C\) for which this phenomenon of regularization develops are examined. The regularizing effect also depends upon the shape of the starting quadrangle. The investigation of such shapes leads into the field of complex dynamics in one variable. Methods of discrete dynamics are employed to explore the regularizing behaviour of the procedure.
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Eberharter, G., Lang, J. & Röschel, O. Regularizing quadrangles in the Möbius plane. J. Geom. 109, 47 (2018). https://doi.org/10.1007/s00022-018-0453-z
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DOI: https://doi.org/10.1007/s00022-018-0453-z