The algebraic dynamics of generic endomorphisms of P^n
Dynamical Systems
2016-01-20 v2
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.
Keywords
Cite
@article{arxiv.1211.7198,
title = {The algebraic dynamics of generic endomorphisms of P^n},
author = {Najmuddin Fakhruddin},
journal= {arXiv preprint arXiv:1211.7198},
year = {2016}
}
Comments
Some details added, results are the same. Final version to appear in Algebra and Number Theory