### Abstract

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 A_{1} ^{(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 language | English |
---|---|

Article number | 095201 |

Pages (from-to) | 095201-095224 |

Number of pages | 24 |

Journal | Journal of Physics. A. Mathematical and Theoretical |

Volume | 48 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2 Mar 2015 |

Externally published | Yes |

### Keywords

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

## Fingerprint Dive into the research topics of 'A systematic approach to reductions of type-Q ABS equations'. Together they form a unique fingerprint.

## Cite this

*Journal of Physics. A. Mathematical and Theoretical*,

*48*(9), 095201-095224. [095201]. https://doi.org/10.1088/1751-8113/48/9/095201