Orbit statistics for algebraic group endomorphisms

We discuss asymptotic counting problems related to the orbit length and the decomposition of orbits into primitive ones, for the action of an endomorphism of an arbitrary algebraic group (such as an elliptic curves, torus, unipotent group,…) over the algebraic closure of a finite field. We present analogues of classical results from number theory related to Mertens’s second theorem and the Erdös-Kac theorem. By making some examples completely explicit, cute transcendental numbers akin the Kempner number make their appearance. (Joint work with Sun Woo Park.)