Full-deautonomisation of a class of second-order mappings in ancillary form

We present an application of the full-deautonomisation method to a class secondorder mappings which, using ancillary variable, can be cast into form that greatly facilitates study their singularities. The approach was originally introduced make it possible construct discrete Painlevé equations associated with affine Weyl group E (1) 8 by deautonomising QRT mapping. has been shown offer practical technique for calculating exact dynamical degree mapping, whereby allowing detection integrability only singularity analysis. confinement property given singularity, wide includes autonomous limit standard additive equation symmetry. This leads non-autonomous mappings, which integrable or not, we obtain degrees. case non-confining is also analysed and again corresponding