QRT Map Research Articles

Integrable mappings via rational elliptic surfaces

We present a geometric description of the QRT map (which is an integrable mapping introduced by Quispel, Roberts and Thompson) in terms of the addition formula of a rational elliptic surface. By this formulation, we classify all the cases when the QRT map is periodic; and show that its period is 2, 3, 4, 5 or 6. A generalization of the QRT map which acts birationally on a pencil of K3 surfaces, or Calabi–Yau manifolds, is also presented.

An alternating integrable map whose square is the QRT map

We present a novel alternating integrable map (i.e., a non-autonomous integrable map whose sole time-dependence is a term of the form (−1) n ). We show that the square (i.e., second iterate) of this map is the QRT map.