43 citations · 119 across the 22 of their papers we have counts for
7 papers · 1 filter
Commutative Poisson algebras from deformations of noncommutative algebras
Alexander V. Mikhailov, Pol Vanhaecke
It is well-known that a formal deformation of a commutative algebra leads to a Poisson bracket on and that the classical limit of a derivation on the…
Integrable maps in 4D and modified Volterra lattices
A. N. W. Hone, J. A. G. Roberts, P. Vanhaecke +1
In recent work, we presented the construction of a family of difference equations associated with the Stieltjes continued fraction expansion of a certain function on a hyperellipti…
A family of integrable maps associated with the Volterra lattice
A. N. W. Hone, J. A. G. Roberts, P. Vanhaecke
Recently Gubbiotti, Joshi, Tran and Viallet classified birational maps in four dimensions admitting two invariants (first integrals) with a particular degree structure, by consider…
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…
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…
Integrable and superintegrable systems associated with multi-sums of products
Peter H. van der Kamp, Theodoros E. Kouloukas, G. R. W. Quispel +2
We construct and study certain Liouville integrable, superintegrable, and non-commutative integrable systems, which are associated with multi-sums of products.
Backlund transformations for finite-dimensional integrable systems: a geometric approach
V. Kuznetsov, P. Vanhaecke
We present a geometric construction of Backlund transformations and discretizations for a large class of algebraic completely integrable systems. To be more precise, we construct f…