Poisson structures for lifts and periodic reductions of integrable 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.

References in corpus (2)

• Yang-Baxter maps: dynamical point of view
• Yang-Baxter maps associated to elliptic curves

Cited by in corpus (5)

• On non-abelian quadrirational Yang-Baxter maps
• Birational solutions to the set-theoretical 4-simplex equation
• Discrete Lax pairs and hierarchies of integrable difference systems
• A Lax pair of a lattice equation whose entropy vanishes
• Noncommutative solutions to Zamolodchikov's tetrahedron equation and matrix six-factorisation problems