From trihomographic to elliptic Painlevé equations. (24th October 2016) - Grammaticos, B; Ramani, A
Abstract: We use the trihomographic representation of discrete Painlevé equations in order to derive a new, factorised form for equations associated with the affine Weyl group E 8 ( 1 ) . Introducing an ancillary dependent variable we are able to obtain factorised forms for the general additive, multiplicative and elliptic discrete E 8 ( 1 ) -related Painlevé equations. The advantage of these factorised forms is that they make the singularity analysis of the E 8 ( 1 ) straightforward in par with the situation for equations associated with lower affine Weyl groups.