On the limits of discrete Painlevé equations associated with the affine Weyl group E$_8$

International audienceWe study the discrete Painlevé equations that can be obtained as limits from the equations associated with the affine Weyl group E(1)8. We obtain equations associated with the groups E(1)7 and E(1)6 as well as linearisable systems. In the E(1)7 and E(1)6 cases, we obtain several new discrete Painlevé equations along with equations which can be related to the ones already known. The same is true for linearisable systems. In the case of new linearisable mappings, we present their explicit linearisation