Could synchrotron light sources benefit from the experience at CERN with beams split in horizontal phase space?

This article reviews the recent activities carried out at CERN in terms of transverse beam splitting with proton beams. Thanks to intense experimental and theoretical activities, the recently-proposed approach of splitting beams in the horizontal phase space using stable islands moved out of the test stage and it became a mature technique of beam manipulation to perform multi-turn extraction. It is therefore timely to address the question whether stable islands can be applied to other branches of accelerator physics, in view of bringing new means of improving ring’s performance. This is the case of synchrotron light machines, where the use of stable islands could lead to new developments, and in this paper options are presented and discussed.