title: Integrable and superintegrable systems associated with multi-sums of products.
abstract: We construct and study certain Liouville integrable, superintegrable and non-commutative integrable systems, which are associated with multi-sums of products.
authors.affiliation: Department of Mathematics , La Trobe University , Bundoora (Melbourne) Victoria 3086, Australia.
authors.forename: Peter H
authors.initials: PH
authors.lastname: van der Kamp
authors.affiliation: Department of Mathematics , La Trobe University , Bundoora (Melbourne) Victoria 3086, Australia.
authors.forename: Theodoros E
authors.initials: TE
authors.lastname: Kouloukas
authors.affiliation: Department of Mathematics , La Trobe University , Bundoora (Melbourne) Victoria 3086, Australia.
authors.forename: G R W
authors.initials: GR
authors.lastname: Quispel
authors.affiliation: Department of Mathematics , La Trobe University , Bundoora (Melbourne) Victoria 3086, Australia.
authors.forename: Dinh T
authors.initials: DT
authors.lastname: Tran
authors.affiliation: Laboratoire de Mathématiques et Applications, UMR 7348 du CNRS , Université de Poitiers , 86962 Futuroscope Chasseneuil Cedex, France.
authors.forename: Pol
authors.initials: P
authors.lastname: Vanhaecke
keywords: Kahan discretization; Lax representation; Lotka–Volterra system; integrable systems; superintegrability