131 citations · 826 across the 43 of their papers we have counts for
43 papers
On the singularity structure of the discrete KdV equation
Doyong Um, Ralph Willox, Basil Grammaticos +1
The discrete KdV (dKdV) equation, the pinnacle of discrete integrability, is often thought to possess the singularity confinement property because it confines on an elementary quad…
Discrete Painlevé equations from singularity patterns: the asymmetric trihomographic case
Basil Grammaticos, Alfred Ramani, Ralph Willox +1
We derive the discrete Painlevé equations associated to the affine Weyl group E that can be represented by an (in the QRT sense) "asymmetric" trihomographic system. The m…
Singularity confinement as an integrability criterion
Takafumi Mase, Ralph Willox, Alfred Ramani +1
In this paper we present a rigorous method for deciding whether a birational three point mapping that has the singularity confinement property is integrable or not, based only on t…
Detecting discrete integrability: the singularity approach
Basil Grammaticos, Alfred Ramani, Ralph Willox +1
We describe the various types of singularities that can arise for second order rational mappings and we discuss the historical and present-day, practical, role the singularity conf…
Singularity patterns and dynamical degrees
Takafumi Mase, Ralph Willox, Alfred Ramani +1
We explain on a selection of mappings how the method introduced by Halburd and our simplified variant thereof, the so-called express method, can be used to calculate the dynamical…
Calculating the algebraic entropy of mappings with unconfined singularities
Alfred Ramani, Basil Grammaticos, Ralph Willox +2
We present a method for calculating the dynamical degree of a mapping with unconfined singularities. It is based on a method introduced by Halburd for the computation of the growth…