Abstract
We derive integrable equations starting from autonomous mappings with a general form inspired by the multiplicative systems associated with the affine Weyl group E8(1). Five such systems are obtained, three of which turn out to be linearisable and the remaining two are integrable in terms of elliptic functions. In the case of the linearisable mappings, we derive non-autonomous forms which contain a free function of the independent variable and we present the linearisation in each case. The two remaining systems are deautonomised to new discrete Painlevé equations. We show that these equations are in fact special forms of much richer systems associated with the affine Weyl groups E7(1) and E8(1), respectively.
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