We present the discrete systems which result from the discrete Painlevé equations q-PVI and d-PV associated to the affine Weyl group E7(1). Two different procedures (“limits” and “degeneracies”) are used, giving rise to a host of new discrete Painlevé equations but also to some...

We investigate the generalisations of the Quispel, Roberts and Thompson (QRT) family of mappings in the plane leaving a rational quadratic expression invariant to the case of four variables. We assume invariance of the rational expression under a cyclic permutation of variables and we impose a...

We analyse the properties of a particular birational mapping of two variables (Cremona transformation) depending on two free parameters (ε and α), associated with the action of a discrete group of non-linear (birational) transformations on the entries of a q × q matrix. This mapping...

We analyse birational mappings generated by transformations on q × q matrices which correspond respectively to two kinds of transformations: the matrix inversion and a permutation of the entries of the q × q matrix. Remarkable factorization properties emerge for quite general involutive...