19 citations · 29 across the 7 of their papers we have counts for
7 papers
New cluster algebras from old: integrability beyond Zamolodchikov periodicity
Andrew N. W. Hone, Wookyung Kim, Takafumi Mase
We consider discrete dynamical systems obtained as deformations of mutations in cluster algebras associated with finite-dimensional simple Lie algebras. The original (undeformed) d…
Deformed cluster maps of type
Jan E. Grabowski, Andrew N. W. Hone, Wookyung Kim
We extend recent work of the third author and Kouloukas by constructing deformations of integrable cluster maps corresponding to the Dynkin types , lifting these to higher-…
Heron triangles and the hunt for unicorns
Andrew N. W. Hone
A Heron triangle is one that has all integer side lengths and integer area, which takes its name from Heron of Alexandria's area formula. From a more relaxed point of view, if resc…
Integrable maps in 4D and modified Volterra lattices
A. N. W. Hone, J. A. G. Roberts, P. Vanhaecke +1
In recent work, we presented the construction of a family of difference equations associated with the Stieltjes continued fraction expansion of a certain function on a hyperellipti…
A family of integrable maps associated with the Volterra lattice
A. N. W. Hone, J. A. G. Roberts, P. Vanhaecke
Recently Gubbiotti, Joshi, Tran and Viallet classified birational maps in four dimensions admitting two invariants (first integrals) with a particular degree structure, by consider…
Some integrable maps and their Hirota bilinear forms
A. N. W. Hone, T. E. Kouloukas, G. R. W. Quispel
We introduce a two-parameter family of birational maps, which reduces to a family previously found by Demskoi, Tran, van der Kamp and Quispel (DTKQ) when one of the parameters is s…