Rubio cubics and generalized Cundy-Parry mappings (Q5962043)

The author studies properties of special mappings of the `transfigured plane of a reference triangle' \(ABC\). He defines two `generalized Rubio mappings' \(\phi\) and \(\psi\) which are based on starting points \(F\) and \(X\), resp. \(U\). He proves that the two mappings are essentially inverse to each other. Then he defines cubics \(Z(F^+)\) and \(Z(F^-)\) associated with \(F\) and shows: \(\phi (Z(F^+)) \subset Z(F^-)\). In the manuscript further properties of these cubics are worked out and discussed.