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arXiv · 1211.7198

The algebraic dynamics of generic endomorphisms of P^n

Najmuddin Fakhruddin
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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.

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Najmuddin Fakhruddin. 2013-07-05. The algebraic dynamics of generic endomorphisms of P^n. https://doi.org/10.2140/ant.2014.8.587

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