5 citations · 5 across the 4 of their papers we have counts for
7 papers
Discrete differential-geometric Poisson brackets: general theory and explicit constructions
Marta Dell'Atti, Giorgio Gubbiotti, Pierandrea Vergallo
We review the discrete theory of differential-geometric Poisson brackets as introduced by B. A. Dubrovin, and we present a complete proof of their characterisation in the non-degen…
Classification of pairs of second-order Hamiltonian operators and hydrodynamic type systems in six components
Giorgio Gubbiotti, Lambertus Van Geemen, Pierandrea Vergallo
Following a recent characterisation of hydrodynamic systems with second-order Hamiltonian structure in terms of alternating three-forms on the projective space, we present a comple…
A novel chain of Lie algebras and its coalgebra symmetry
Giorgio Gubbiotti, Danilo Latini, Bert van Geemen
We study a novel -dimensional non-semisimple Lie algebra , a generalisation of both and the two-photon Lie algebra $\mathfra…
Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators
Giorgio Gubbiotti, Francesco Oliveri, Emanuele Sgroi +1
We study from an algebraic and geometric viewpoint Hamiltonian operators which are sum of a non-degenerate first-order homogeneous operator and a Poisson tensor. In flat coordinate…
The Painlevé equivalence problem for a constrained 3D system
Galina Filipuk, Michele Graffeo, Giorgio Gubbiotti +1
In this paper we propose a geometric approach to study Painlevé equations appearing as constrained systems of three first-order ordinary differential equations. We illustrate this…
Line geometry of pairs of second-order Hamiltonian operators and quasilinear systems
Giorgio Gubbiotti, Bert van Geemen, Pierandrea Vergallo
We demonstrate that a pair consisting of a second-order homogeneous Hamiltonian structure in components and its associated system of conservation laws is in bijective correspon…
An Elementary Construction of Modified Hamiltonians and Modified Measures of 2D Kahan Maps
Giorgio Gubbiotti, David McLaren, G. R. W. Quispel
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 expre…