Poisson structures for lifts and periodic reductions of integrable lattice equations

TL;DR

This paper develops Poisson structures for four-dimensional maps obtained from integrable lattice equations, ensuring these maps are Poisson and have involutive integrals, advancing the understanding of their integrability properties.

Contribution

The paper introduces new Poisson structures for lifts and periodic reductions of integrable lattice equations, demonstrating their Poisson nature and involutive integrals.

Findings

Maps are Poisson with respect to the new structures

Integrals are in involution

Advances understanding of integrability in lattice equations

Abstract

We introduce and study suitable Poisson structures for four dimensional maps derived as lifts and specific periodic reductions of integrable lattice equations. These maps are Poisson with respect to these structures and the corresponding integrals are in involution.