Euclidean Skolem-Mahler-Lech-Chabauty方法
A Euclidean Skolem-Mahler-Lech-Chabauty method
摘要：
利用o-极小性理论，我们证明了Skolem-Mahler-Lech-Chabauty的$p$ -adic方法可以适用于某些实解析动力系统的动力学Mordell-Lang猜想的证明.例如，我们表明，如果$f_1,...,f_n$是一个有限序列的实际解析函数$f_i:(-1,1) \to (-1,1)$的$f_i(0) = 0$和$|f_i'(0)| \leq 1$（可能为零），$a = (a_1,...,a_n)$是一个$n$元组的实数足够接近的起源和$H(x_1,...,x_n)$是一个真正的解析函数的$n$变量，然后设置$\{m \in {\mathbb N} : H (f_1^{\circ m} (a_1),...,f_n^{\circ m}(a_n)) = 0 \}$是所有的${\mathbb N}$，所有的奇数，所有的偶数，或有限的。
英文摘要：
Using the theory of o-minimality we show that the $p$-adic method of Skolem-Mahler-Lech-Chabauty may be adapted to prove instances of the dynamical Mordell-Lang conjecture for some real analytic dynamical systems. For example, we show that if $f_1,...,f_n$ is a finite sequence of real analytic functions $f_i:(-1,1) \to (-1,1)$ for which $f_i(0) = 0$ and $|f_i'(0)| \leq 1$ (possibly zero), $a = (a_1,...,a_n)$ is an $n$-tuple of real numbers close enough to the origin and $H(x_1,...,x_n)$ is a real analytic function of $n$ variables, then the set $\{m \in {\mathbb N} : H (f_1^{\circ m} (a_1),...,f_n^{\circ m}(a_n)) = 0 \}$ is either all of ${\mathbb N}$, all of the odd numbers, all of the even numbers, or is finite.
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