Zobrazeno 1 - 10
of 60
pro vyhledávání: '"Gubbiotti, Giorgio"'
We show that a pair formed by a second-order homogeneous Hamiltonian structures in $N$ components and the associated system of conservation laws is in bijective correspondence with an alternating three-form on a $N+2$ vector space. We use this result
Externí odkaz:
http://arxiv.org/abs/2403.09152
Hex systems were recently introduced [A. P. Kels. Integrable systems on hexagonal lattices and consistency on polytopes with quadrilateral and hexagonal faces. 2022. arXiv:2205.02720 [math-ph]] as systems of equations defined on two-dimensional honey
Externí odkaz:
http://arxiv.org/abs/2311.01359
Publikováno v:
Open Communications in Nonlinear Mathematical Physics, Special Issue in Memory of Decio Levi (March 1, 2024) ocnmp:12249
We show how to construct in an elementary way the invariant of the KHK discretisation of a cubic Hamiltonian system in two dimensions. That is, we show that this invariant is expressible as the product of the ratios of affine polynomials defining the
Externí odkaz:
http://arxiv.org/abs/2309.00799
Autor:
Gubbiotti, Giorgio
Publikováno v:
Open Communications in Nonlinear Mathematical Physics, Special Issue in Memory of Decio Levi (February 15, 2024) ocnmp:11638
In this work I discuss briefly the calculation of the algebraic entropy for systems of quad equations. In particular, I observe that since systems of multilinear equations can have algebraic solution, in some cases one might need to restrict the dire
Externí odkaz:
http://arxiv.org/abs/2307.12314
Autor:
Gubbiotti, Giorgio, Shi, Yang
We determine the affine Weyl symmetries of some two-dimensional birational maps known as QRT roots arising from Kahan--Hirota--Kimura discretisation of two different reduced Nahm systems. The main finding is that the symmetry types of these discrete
Externí odkaz:
http://arxiv.org/abs/2305.17107
Autor:
Graffeo, Michele, Gubbiotti, Giorgio
Motivated by the study of the Kahan--Hirota--Kimura discretisation of the Euler top, we characterise the growth and integrability properties of a collection of elements in the Cremona group of a complex projective 3-space using techniques from algebr
Externí odkaz:
http://arxiv.org/abs/2301.09129
The $\mathfrak{sl}_{2}(\mathbb{R})$ coalgebra symmetry and the superintegrable discrete-time systems
Autor:
Gubbiotti, Giorgio, Latini, Danilo
Publikováno v:
Phys. Scr. 98 045209, 2023
In this paper, we classify all the variational discrete-time systems in quasi-standard form in $N$ degrees of freedom admitting coalgebra symmetry with respect to the generic realisation of the Lie-Poisson algebra $\mathfrak{sl}_{2}(\mathbb{R})$. Thi
Externí odkaz:
http://arxiv.org/abs/2210.17171
We study properties of Hamiltonian integrable systems with random initial data by considering their Lax representation. Specifically, we investigate the spectral behaviour of the corresponding Lax matrices when the number $N$ of degrees of freedom of
Externí odkaz:
http://arxiv.org/abs/2206.15371
Autor:
Gubbiotti, Giorgio, Kels, Andrew P.
Publikováno v:
J. Phys. A: Math. Theor. 54 (2021) 455201
In this paper we define the algebraic entropy test for face-centered quad equations, which are equations defined on vertices of a quadrilateral plus an additional interior vertex. This notion of algebraic entropy is applied to a recently introduced c
Externí odkaz:
http://arxiv.org/abs/2105.12404
Autor:
Gubbiotti, Giorgio
We use a recently found method to characterise all the invertible fourth-order difference equations linear in the extremal values based on the existence of a discrete Lagrangian. We also give some result on the integrability properties of the obtaine
Externí odkaz:
http://arxiv.org/abs/1910.11458