Re-factorising a QRT map
arXiv:1906.00501
Abstract
A QRT map is the composition of two involutions on a biquadratic curve: one switching the -coordinates of two intersection points with a given horizontal line, and the other switching the -coordinates of two intersections with a vertical line. Given a QRT map, a natural question is to ask whether it allows a decomposition into further involutions. Here we provide new answers to this question and show how they lead to a new class of maps, as well as known HKY maps and quadrirational Yang-Baxter maps.
17 pages