4 papers
Singularity interactions for lattice equations: introducing the taishi
Ralph Willox, Basil Grammaticos, Alfred Ramani +1
We study the singularities of some selected integrable lattice equations and show they all admit three types of singularities: one of finite and two of infinite extent. In particul…
Deautonomising the Lyness mapping
Basil Grammaticos, Alfred Ramani, Ralph Willox
We examine the Lyness mapping (an integrable th-order discrete system which can be generated from a one-dimensional reduction of the Hirota-Miwa equation) from the point of view…
The trouble with deautonomising higher order maps
Ralph Willox, Basil Grammaticos, Alfred Ramani
The deautonomisation of birational maps that have the singularity confinement property, i.e. the construction of nonautonomous versions of such maps that preserve the singularity p…
A fast algorithmic way to calculate the degree growth of birational mappings
Basil Grammaticos, Alfred Ramani, Adrian Stefan Carstea +1
We present an algorithmic method for the calculation of the degrees of the iterates of birational mappings, based on Halburd's method for obtaining the degrees from the singularity…