Re-factorising a QRT map

Nalini Joshi; Pavlos Kassotakis

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arXiv · 1906.00501

Re-factorising a QRT map

Nalini Joshi·Pavlos Kassotakis

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Abstract

A QRT map is the composition of two involutions on a biquadratic curve: one switching the $x$-coordinates of two intersection points with a given horizontal line, and the other switching the $y$-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.

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Nalini Joshi, Pavlos Kassotakis. 2019-06-02. Re-factorising a QRT map. https://arxiv.org/abs/1906.00501

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