arXiv subjects

P. Adamopoulou

Publications and source records attributed to P. Adamopoulou.

3 recordsLinked to original sources

arXiv2025

Reductions and degenerate limits of Yang-Baxter maps with $3\times 3$ Lax matrices

We generalise a family of quadrirational parametric Yang-Baxter maps with $3\times 3$ Lax matrices by introducing additional essential parameters. These maps preserve a prescribed Poisson structure which originates from the Sklyanin bracket. We investigate various low-dimensional reductions of this family, as well as degenerate limits with respect to the parameters that were introduced. As a result, we derive several birational Yang-Baxter maps, and we discuss some of their integrability properties. This work is part of a more general classification of Yang-Baxter maps admitting a strong $3\times 3$ Lax matrix with a linear dependence on the spectral parameter.

nlin.SI↗

arXiv2023

Entwining Yang-Baxter maps over Grassmann algebras

We construct novel solutions to the set-theoretical entwining Yang-Baxter equation. These solutions are birational maps involving non-commutative dynamical variables which are elements of the Grassmann algebra of order $n$. The maps arise from refactorisation problems of Lax supermatrices associated to a nonlinear Schrödinger equation. In this non-commutative setting, we construct a spectral curve associated to each of the obtained maps using the characteristic function of its monodromy supermatrix. We find generating functions of invariants (first integrals) for the entwining Yang-Baxter maps from the moduli of the spectral curves. Moreover, we show that a hierarchy of birational entwining Yang-Baxter maps with commutative variables can be obtained by fixing the order $n$ of the Grassmann algebra. We present the members of the hierarchy in the case $n=1$ (dual numbers) and $n=2$, and discuss their dynamical and integrability properties, such as Lax matrices, invariants, and measure preservation.

nlin.SI↗

arXiv2020

Integrable extensions of Adler's map via Grassmann algebras

We study certain extensions of the Adler map on Grassmann algebras $Γ(n)$ of order $n$. We consider a known Grassmann-extended Adler map, and assuming that $n=1$ we obtain a commutative extension of Adler's map in six dimensions. We show that the map satisfies the Yang--Baxter equation, admits three invariants and is Liouville integrable. We solve the map explicitly, viewed as a discrete dynamical system.

nlin.SI↗