Arithmetic dynamics on smooth cubic surfaces
arXiv:1307.3205
Abstract
We study dynamical systems induced by birational automorphisms on smooth cubic surfaces defined over a number field . 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 and -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.
22 pages changes in v2: * major streamlining + many fixes to typos * correction to Corollary in Section 8