4 papers
Commuting integrable maps from a deformed D cluster algebra
A. N. W. Hone, W. Kim, T. Mase
In this paper we revisit an integrable map of the plane which we obtained recently as a two-parameter family of deformed mutations in the cluster algebra of type D. The rationa…
Integrable deformations of cluster maps of type
Wookyung Kim
In this paper, we extend one of the main results from our joint work with Hone and Mase, in which we studied a deformed type map, to the general case of the type f…
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-…