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摘要翻译：
设$(K,\cdot)$是一个完全的离散值域，$f:{\mathbb B}_1(K,1)\到{\mathbb B}_1(K,1)$是一个从单元返回到它自身的非常解析映射。我们假设0是$F$的吸引不动点。设$a\在K$中具有$\lim_{n\to\infty}f^n(a)=0$，并考虑轨道${\mathcal O}_f(a):=\{f^n(a):n\in{\mathbb n}\}$。我们证明了如果0是一个\emph{超吸引}不动点，则在解析Zariski稠密集中的${\mathbb B}_n(K,1)$满足${\mathcal O}_f(a)^n$的每一个不可约解析子簇都由$x_i=B$和$x_j=f^\ell(x_k)$等式定义。当0是吸引点，非超吸引点时，我们证明了所有的解析关系都来自代数环面。
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英文标题：
《Analytic relations on a dynamical orbit》
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作者：
Thomas Scanlon
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Dynamical Systems 动力系统
分类描述：Dynamics of differential equations and flows, mechanics, classical few-body problems, iterations, complex dynamics, delayed differential equations
微分方程和流动的动力学，力学，经典的少体问题，迭代，复杂动力学，延迟微分方程
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一级分类：Mathematics 数学
二级分类：Number Theory 数论
分类描述：Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数，丢番图方程，解析数论，代数数论，算术几何，伽罗瓦理论
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英文摘要：
Let $(K,|\cdot|)$ be a complete discretely valued field and $f:{\mathbb B}_1(K,1) \to {\mathbb B}_1(K,1)$ a nonconstant analytic map from the unit back to itself. We assume that 0 is an attracting fixed point of $f$. Let $a \in K$ with $\lim_{n \to \infty} f^n(a) = 0$ and consider the orbit ${\mathcal O}_f(a) := \{f^n(a) : n \in {\mathbb N} \}$. We show that if 0 is a \emph{superattracting} fixed point, then every irreducible analytic subvariety of ${\mathbb B}_n(K,1)$ meeting ${\mathcal O}_f(a)^n$ in an analytically Zariski dense set is defined by equations of the form $x_i = b$ and $x_j = f^\ell(x_k)$. When 0 is an attracting, non-superattracting point, we show that all analytic relations come from algebraic tori.
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PDF链接：
https://arxiv.org/pdf/0807.4162
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