Invariant volume form for 3D QRT maps

2025/10/13 by Alonso, Jaume, Suris, Yuri B.
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2510.11468

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 P³. 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.

Citations

• Discrete Painlevé equations from pencils of quadrics in \mathbb P³ with branching generators
• On the Hamiltonian structure of Hirota-Kimura discretization of the Euler top

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• Re-factorising a QRT map
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