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We study dynamical systems induced by birational automorphisms on smooth cubic surfaces defined over a number field K. In particular we are interested in the product of non-commuting birational Geiser involutions of the cubic surface. We present results describing the sets of K and K̅-periodic points of the system, and give a necessary and sufficient condition for a dynamical local-global property called strong residual periodicity. Finally, we give a dynamical result relating to the Mordell--Weil problem on cubic surfaces.arXiv:1307.3205v2 fatcat:mnrlapvnvza2vjxrfmtya32p5a