28 citations · 37 across the 9 of their papers we have counts for
9 papers
A construction of solutions of an integrable deformation of a commutative Lie algebra of skew hermitian -matrices
Aloysius Helminck, Gerardus Helminck
Inside the algebra of -matrices with coefficients from a commutative -algebra that have only a finite number of n…
Strict versions of various matrix hierarchies related to SL(n)-loops and their combinations
Gerard Helminck
Let be a commutative Lie subalgebra of of maximal dimension. We consider in this paper three spaces of -loops that each get…
The strict AKNS hierarchy: its structure and solutions
Gerard Helminck
In this paper we discuss an integrable hierarchy of compatible Lax equations that is obtained by a wider deformation of a commutative algebra in the loop space of th…
Newton flows for elliptic functions IV, Pseudo Newton graphs: bifurcation & creation of flows
G. F. Helminck, F. Twilt
An elliptic Newton flow is a dynamical system that can be interpreted as a continuous version of Newton's iteration method for finding the zeros of an elliptic function f. Previous…
Newton flows for elliptic functions II Structural stability: Classification & Representation
G. F. Helminck, F. Twilt
In our previous paper we associated to each non-constant elliptic function on a torus a dynamical system, the elliptic Newton flow corresponding to . We characterized th…
Newton flows for elliptic functions III Classification of order Newton graphs
G. F. Helminck, F. Twilt
A Newton graph of order is a cellularly embedded toroidal graph on vertices, edges and faces that fulfils certain combinatorial properties (Euler, Ha…