Invariant volume form for 3D QRT maps

Abstract

Recently, we proposed a three-dimensional generalization of QRT maps. These novel maps can be associated with pairs of pencils of quadrics in ${\mathbb{P}}^3$. By construction, these maps have two rational integrals (parameters of both pencils). In the present paper, we find an invariant volume form for these maps, thus finally establishing their integrability.

14 pp