42 citations · 213 across the 25 of their papers we have counts for
27 papers
Multicomponent pentagon maps
Pavlos Kassotakis
We provide necessary and sufficient conditions for maps that satisfy associative-like conditions on families of n-ary magmas to be pentagon maps. We obtain parametric-pentagon maps…
Idempotent compatible maps and discrete integrable systems on the triangular lattice
Pavlos Kassotakis, Maciej Nieszporski
We present three equivalence classes of rational non-invertible multidimensional compatible maps. These maps turns out to be idempotent and by construction they admit birational pa…
On refactorization problems and rational Lax matrices of quadrirational Yang-Baxter maps
Pavlos Kassotakis, Theodoros E. Kouloukas, Maciej Nieszporski
We present rational Lax representations for one-component parametric quadrirational Yang-Baxter maps in both the abelian and non-abelian settings. We show that from the Lax matrice…
Non-Abelian elastic collisions, associated difference systems of equations and discrete analytic functions
Pavlos Kassotakis, Theodoros Kouloukas, Maciej Nieszporski
We extend the equations of motion that describe non-relativistic elastic collision of two particles in one dimension to an arbitrary associative algebra. Relativistic elastic colli…
Entwining tetrahedron maps
Pavlos Kassotakis
We present three non-equivalent procedures to obtain entwining (non-constant) tetrahedron maps. Given a tetrahedron map, the first procedure incorporates its underlying symmetry gr…
On quadrirational pentagon maps
Charalampos Evripidou, Pavlos Kassotakis, Anastasios Tongas
We classify rational solutions of a specific type of the set theoretical version of the pentagon equation. That is, we find all quadrirational maps $R:(x,y)\mapsto (u(x,y),v(x,y)),…
Matrix factorizations and pentagon maps
Pavlos Kassotakis
We propose a specific class of matrices which participate in factorization problems that turn to be equivalent to constant and entwining (non-constant) pentagon, reverse-pentagon o…
Non-Abelian hierarchies of compatible maps, associated integrable difference systems and Yang-Baxter maps
Pavlos Kassotakis
We present two non-equivalent families of hierarchies of non-Abelian compatible maps and we provide their Lax pair formulation. These maps are associated with families of hierarchi…
On non-abelian quadrirational Yang-Baxter maps
Pavlos Kassotakis, Theodoros Kouloukas
We introduce four lists of families of non-abelian quadrirational Yang-Baxter maps.
Kahan discretizations of skew-symmetric Lotka-Volterra systems and Poisson maps
Charalampos Evripidou, Pavlos Kassotakis, Pol Vanhaecke
The Kahan discretization of the Lotka-Volterra system, associated with any skew-symmetric graph , leads to a family of rational maps, parametrized by the step size. When these m…
Discrete Lax pairs and hierarchies of integrable difference systems
Pavlos Kassotakis
We introduce a family of order Lax matrices that is indexed by the natural number For each value of they serve as strong Lax matrices…
Morphisms and automorphisms of skew-symmetric Lotka-Volterra systems
Charalampos Evripidou, Pavlos Kassotakis, Pol Vanhaecke
We study the basic relation between skew-symmetric Lotka-Volterra systems and graphs, both at the level of objects and morphisms, and derive a classification from it of skew-symmet…
Tetrahedron maps and symmetries of three dimensional integrable discrete equations
Pavlos Kassotakis, Maciej Nieszporski, Vassilios Papageorgiou +1
A relationship between the tetrahedron equation for maps and the consistency property of integrable discrete equations on is investigated. Our approach is a generali…
Integrable multi-component difference systems of equations
Pavlos Kassotakis, Maciej Nieszporski, Vassilios Papageorgiou +1
We present two lists of multi-component systems of integrable difference equations defined on the edges of a graph. The integrability of these systems is manifested…
Systems of difference equations on a vector valued function that admit 3D space of scalar potentials
Pavlos Kassotakis, Maciej Nieszporski
For some involutive maps we find all invariants with separated variables. We investigate a link of…
Re-factorising a QRT map
Nalini Joshi, Pavlos Kassotakis
A QRT map is the composition of two involutions on a biquadratic curve: one switching the -coordinates of two intersection points with a given horizontal line, and the other swi…
Integrable reductions of the dressing chain
Charalampos Evripidou, Pavlos Kassotakis, Pol Vanhaecke
In this paper we construct a family of integrable reductions of the dressing chain, described in its Lotka-Volterra form. For each with we obtai…
Invariants in Separated Variables: Yang-Baxter, Entwining and Transfer Maps
Pavlos Kassotakis
We present the explicit form of a family of Liouville integrable maps in 3 variables, the so-called triad family of maps and we propose a multi-field generalisation of the latter.…
Difference systems in bond and face variables and non-potential versions of discrete integrable systems
Pavlos Kassotakis, Maciej Nieszporski
Integrable discrete scalar equations defined on a~two or a three dimensional lattice can be rewritten as difference systems in bond variables or in face variables respectively. Bot…
Integrable deformations of the Bogoyavlenskij-Itoh Lotka-Volterra systems
Charalampos Evripidou, Pavlos Kassotakis, Pol Vanhaecke
We construct a family of integrable deformations of the Bogoyavlenskij-Itoh systems and construct a Lax operator with spectral parameter for it. Our approach is based on the constr…
Integrable reductions of the Bogoyavlenskij-Itoh Lotka-Volterra systems
Pantelis A. Damianou, Charalampos A. Evripidou, Pavlos Kassotakis +1
Given a constant skew-symmetric matrix A, it is a difficult open problem whether the associated Lotka-Volterra system is integrable or not. We solve this problem in the special cas…
rational maps
Pavlos Kassotakis, Maciej Nieszporski, Pantelis Damianou
We present a natural extension of the notion of nondegenerate rational maps (quadrirational maps) to arbitrary dimensions. We refer to these maps as rational maps. In this no…
A Lax pair for the complete QRT mapping
P. Howes, N. Joshi, P. Kassotakis
QRT maps are translations on smooth biquadratic curves, also known as elliptic curves. Special cases of QRT maps are known to arise as compatibility conditions for an associated sy…
Integrable Maps which Preserve Functions with Symmetries
Allan P Fordy, Pavlos Kassotakis
We consider maps which preserve functions which are built out of the invariants of some simple vector fields. We give a reduction procedure, which can be used to derive commuting m…