Poisson Yang-Baxter maps with binomial Lax matrices

Abstract

A construction of multidimensional parametric Yang-Baxter maps is presented. The corresponding Lax matrices are the symplectic leaves of first degree matrix polynomials equipped with the Sklyanin bracket. These maps are symplectic with respect to the reduced symplectic structure on these leaves and provide examples of integrable mappings. An interesting family of quadrirational symplectic YB maps on ${\mathbb{C}}^4\times {\mathbb{C}}^4$ with $3\times 3$ Lax matrices is also presented.

22 pages, 3 figures

References in corpus (1)

• Yang Baxter maps with first degree polynomial 2 by 2 Lax matrices

Cited by in corpus (17)

• Darboux transformations, finite reduction groups and related Yang-Baxter maps
• Integrable Euler top and nonholonomic Chaplygin ball
• Grassmann extensions of Yang-Baxter maps
• A noncommutative discrete potential KdV lift
• On the $3D$ consistency of a Grassmann extended lattice Boussinesq system
• Poisson structures for lifts and periodic reductions of integrable lattice equations
• Yang--Baxter maps, Darboux transformations, and linear approximations of refactorisation problems
• Entwining Yang-Baxter maps related to NLS type equations
• Relativistic Collisions as Yang-Baxter maps
• Algebraic and differential-geometric constructions of set-theoretical solutions to the Zamolodchikov tetrahedron equation
• Local Yang--Baxter correspondences and set-theoretical solutions to the Zamolodchikov tetrahedron equation
• Soliton interactions and Yang-Baxter maps for the complex coupled short-pulse equation
• Tetrahedron maps, Yang-Baxter maps, and partial linearisations
• Second-order Symmetric Non-negative Latent Factor Analysis
• Breather interactions in the integrable discrete Manakov system and trigonometric Yang-Baxter maps
• Discrete integrable systems, Darboux transformations, and Yang-Baxter maps
• On refactorization problems and rational Lax matrices of quadrirational Yang-Baxter maps