动力序列：闭包性质和自动恒等式证明
Dynamical sequences: closure properties and automatic identity proving
AI总结：
本文研究了动力序列的闭包性质，展示了其涵盖多种经典序列，并提出算法证明动力序列恒等式。
摘要：
给定一个代数闭合的域K，一个动力序列是形如a(n):=f(ϕ^n(x_0))的K值序列，其中ϕ: X→X和f: X→A^1是定义在K上的有理映射，且x_0∈X是一个点，其正向轨道避免了ϕ和f的不确定性区域。许多经典数论和代数组合学中的序列都属于这一动力框架，我们展示了动力序列的类别具有许多闭包性质，并涵盖了所有椭圆除数序列、所有Somos序列以及所有C^n-和D^n-有限序列（对于所有n≥1），如Jiménez-Pastor、Nuspl和Pillwein所定义。我们还提供了一个证明两个动力序列相等的算法，并通过展示如何用此算法证明几个经典组合恒等式来说明其使用方法。
英文摘要：
Given an algebraically closed field $K$, a dynamical sequence over $K$ is a $K$-valued sequence of the form $a(n):= f(ϕ^n(x_0))$, where $ϕ\colon X\to X$ and $f\colon X\to\mathbb{A}^1$ are rational maps defined over $K$, and $x_0\in X$ is a point whose forward orbit avoids the indeterminacy loci of $φ$ and $f$. Many classical sequences from number theory and algebraic combinatorics fall under this dynamical framework, and we show that the class of dynamical sequences enjoys numerous closure properties and encompasses all elliptic divisibility sequences, all Somos sequences, and all $C^n$- and $D^n$-finite sequences for all $n\ge 1$, as defined by Jiménez-Pastor, Nuspl, and Pillwein. We also give an algorithm for proving that two dynamical sequences are identical and illustrate how to use this algorithm by showing how to prove several classical combinatorial identities via this method.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
