The algebraic dynamics of generic endomorphisms of ℙn
The algebraic dynamics of generic endomorphisms of ℙn
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DOI：
10.2140/ant.2014.8.587
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发表时间：
2012-11
影响因子：
1.3
通讯作者：
N. Fakhruddin
中科院分区：
文献类型：
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作者：
N. Fakhruddin
在特征零域上射影空间的一般自同态情形下，研究了代数动力学中的一些一般性问题。我们证明的主要结果是：一般自同态没有非平凡的预周期子簇，任何无限的预周期点集都是Zariski稠密的，单轨道的任何无限子集也是Zariski稠密的，从而验证了张的动力学“Manin-Mumford”猜想和这种情况下Denis和Ghioca-Tucker的动力学“Mordell-Lang”猜想.
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.