Abstract:

Recently, many papers have considered so-called non-QRT birational maps of the plane. Compared to the QRT family of maps which preserve each biquadratic curve in a fibration of the plane, non-QRT maps send a biquadratic curve to another biquadratic curve belonging to the same fibration or to a curve in a different fibration. In this talk, we give the general form of a birational map derived from a second order difference equation that sends a biquadratic curve to another and give the necessary and sufficient condition for such a map to exist.