19 citations · 135 across the 25 of their papers we have counts for
29 papers
Algebraic entropy for systems of quad equations
Giorgio Gubbiotti
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…
Determination of the symmetry group for some QRT roots
Giorgio Gubbiotti, Yang Shi
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 s…
Growth and integrability of some birational maps in dimension three
Michele Graffeo, Giorgio Gubbiotti
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 Crem…
The coalgebra symmetry and the superintegrable discrete-time systems
Giorgio Gubbiotti, Danilo Latini
In this paper, we classify all the variational discrete-time systems in quasi-standard form in degrees of freedom admitting coalgebra symmetry with respect to the generic reali…
Discrete integrable systems and random Lax matrices
Massimo Gisonni, Tamara Grava, Giorgio Gubbiotti +1
We study properties of Hamiltonian integrable systems with random initial data by considering their Lax representation. Specifically, we investigate the spectral behaviour of the c…
Coalgebra symmetry for discrete systems
G. Gubbiotti, D. Latini, B. K. Tapley
In this paper we introduce the notion of coalgebra symmetry for discrete systems. With this concept we prove that all discrete radially symmetric systems in standard form are quasi…
Algebraic entropy for face-centered quad equations
Giorgio Gubbiotti, Andrew P. Kels
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.…
Superintegrable systems in non-Euclidean plane: hidden symmetries leading to linearity
G. Gubbiotti, M. C. Nucci
Nineteen classical superintegrable systems in two-dimensional non-Euclidean spaces are shown to possess hidden symmetries leading to their linearization. They are the two Perlick s…
Lax pairs for the discrete reduced Nahm systems
G. Gubbiotti
We discretise the Lax pair for the reduced Nahm systems and prove its equivalence with the Kahan-Hirota-Kimura discretisation procedure. We show that these Lax pairs guarantee the…
Space of initial values of a map with a quartic invariant
G. Gubbiotti, N. Joshi
We compactify and regularize the space of initial values of a planar map with a quartic invariant and use this construction to prove its integrability in the sense of algebraic ent…
Lagrangians and integrability for additive fourth-order difference equations
Giorgio Gubbiotti
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. W…
Algebraic entropy of a class of five-point differential-difference equations
G. Gubbiotti
We compute the algebraic entropy of a class of integrable Volterra-like five-point differential-difference equations recently classified using the generalised symmetry method. We s…
Integrable discrete autonomous quad-equations admitting, as generalized symmetries, known five-point differential-difference equations
R. N. Garifullin, G. Gubbiotti, R. I. Yamilov
In this paper we construct the autonomous quad-equations which admit as symmetries the five-point differential-difference equations belonging to known lists found by Garifullin, Ya…
On the inverse problem of the discrete calculus of variations
G. Gubbiotti
In this paper we present an algorithm to find the discrete Lagrangian for an autonomous recurrence relation of arbitrary even order with . The method is based on the exis…
Complexity and integrability in 4D bi-rational maps with two invariants
G. Gubbiotti, N. Joshi, D. T. Tran +1
In this letter we give fourth-order autonomous recurrence relations with two invariants, whose degree growth is cubic or exponential. These examples contradict the common belief th…
A multiple scales approach to maximal superintegrability
G. Gubbiotti, D. Latini
In this paper we present a simple, algorithmic test to establish if a Hamiltonian system is maximally superintegrable or not. This test is based on a very simple corollary of a the…
Reconstructing a Lattice Equation: a Non-Autonomous Approach to the Hietarinta Equation
Giorgio Gubbiotti, Christian Scimiterna
In this paper we construct a non-autonomous version of the Hietarinta equation [Hietarinta J., J. Phys. A: Math. Gen. 37 (2004), L67-L73] and study its integrability properties. We…
Darboux Integrability of Trapezoidal and Families of Lattice Equations II: General Solutions
Giorgio Gubbiotti, Christian Scimiterna, Ravil I. Yamilov
In this paper we construct the general solutions of two families of quad-equations, namely the trapezoidal equations and the equations. These solutions are obtained…
Darboux integrability of trapezoidal and families of lattice equations I: First integrals
G. Gubbiotti, R. I. Yamilov
In this paper we prove that the trapezoidal and the families of quad-equations are Darboux integrable systems. This result sheds light on the fact that such equatio…
Quantization of the dynamics of a particle on a double cone by preserving Noether symmetries
G. Gubbiotti, M. C. Nucci
The classical quantization of the motion of a free particle and that of an harmonic oscillator on a double cone are achieved by a quantization scheme [M.C. Nucci, Theor. Math. Phys…
Algebraic entropy, symmetries and linearization of quad equations consistent on the cube
Giorgio Gubbiotti, Christian Scimiterna, Decio Levi
We discuss the non autonomous nonlinear partial difference equations belonging to Boll classification of quad graph equations consistent around the cube. We show how starting from…
Thermodynamics of slow solutions to the Gas-Piston equations
G. Gubbiotti, D. Chiuchiù
Despite its historical importance, a perfect gas enclosed by a pistons and in contact with a thermal reservoirs is a system still largely under study. Its thermodynamic properties…
Are all classical superintegrable systems in two-dimensional space linearizable?
G. Gubbiotti, M. C. Nucci
Several examples of classical superintegrable systems in two-dimensional spac are shown to possess hidden symmetries leading to their linearization. They are those determined 50 ye…
On Partial Differential and Difference Equations with Symmetries Depending on Arbitrary Functions
Giorgio Gubbiotti, Decio Levi, Christian Scimiterna
In this note we present some ideas on when Lie symmetries, both point and generalized, can depend on arbitrary functions. We show on a few examples, both in partial differential an…