33 citations · 192 across the 30 of their papers we have counts for
6 papers · 1 filter
Algebraic entropy of a multi-term recurrence of the Hietarinta-Viallet type
Ryo Kamiya, Masataka Kanki, Takafumi Mase +1
We introduce a family of extensions of the Hietarinta-Viallet equation to a multi-term recurrence relation via a reduction from the coprimeness-preserving extension to the discrete…
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…
On the Coprimeness Property of Discrete Systems without the Irreducibility Condition
Masataka Kanki, Takafumi Mase, Tetsuji Tokihiro
In this article we investigate the coprimeness properties of one and two-dimensional discrete equations, in a situation where the equations are decomposable into several factors of…
Toda type equations over multi-dimensional lattices
Ryo Kamiya, Masataka Kanki, Takafumi Mase +2
We introduce a class of recursions defined over the -dimensional integer lattice. The discrete equations we study are interpreted as higher dimensional extensions to the discret…