29 citations · 287 across the 41 of their papers we have counts for
4 papers · 2 filters
Restoring discrete Painlevé equations from an E-associated one
Basil Grammaticos, Alfred Ramani, Ralph Willox
We present a systematic method for the construction of discrete Painlevé equations. The method, dubbed `restoration', allows one to obtain all discrete Painlevé equations that shar…
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…