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 nontrivial 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 and Tucker in this case.
Citation
Najmuddin Fakhruddin. "The algebraic dynamics of generic endomorphisms of $\mathbb{P}^n$." Algebra Number Theory 8 (3) 587 - 608, 2014. https://doi.org/10.2140/ant.2014.8.587
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