The algebraic dynamics of generic endomorphisms of P^n

Abstract

We investigate some general questions in algebraic dynamics in the case of generic endomorphisms of projective spaces over a field of characteristic zero. The main results that we prove are that a generic endomorphism has no non-trivial preperiodic subvarieties, any infinite set of preperiodic points is Zariski dense and any infinite subset of a single orbit is also Zariski dense, thereby verifying the dynamical "Manin--Mumford" conjecture of Zhang and the dynamical "Mordell--Lang" conjecture of Denis and Ghioca--Tucker in this case.

Some details added, results are the same. Final version to appear in Algebra and Number Theory

Cited by in corpus (2)

• The existence of Zariski dense orbits for polynomial endomorphisms of the affine plane
• Algebraic dynamics of the lifts of Frobenius