A systematic approach to reductions of type-Q ABS equations

Mike Hay, Phil Howes, Nobutaka Nakazono, Yang Shi

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


We present a class of reductions of Möbius type for the lattice equations known as Q1, Q2, and Q3 from the ABS list. The deautonomized form of one particular reduction of Q3 is shown to exist on the A1 (1)surface which belongs to the multiplicative type of rational surfaces in Sakais classification of Painlevé systems. Using the growth of degrees of iterates, all other mappings that result from the class of reductions considered here are shown to be linearizable. Any possible linearizations are calculated explicitly by constructing a birational transformation defined by invariant curves in the blown up space of initial values for each reduction.

Original languageEnglish
Article number095201
Pages (from-to)095201-095224
Number of pages24
JournalJournal of Physics. A. Mathematical and Theoretical
Issue number9
Publication statusPublished - 2 Mar 2015
Externally publishedYes


  • lattice equations
  • ABS equations
  • discrete Painleve equation
  • similarity reductions
  • discrete Painlev equations


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