论文标题
部分可观测时空混沌系统的无模型预测
Effective bounds on $S$-integral preperiodic points for polynomials
论文作者
论文摘要
考虑到在数字字段$ k $上定义的多项式$ f $，我们对S. IH的某些特殊情况有效，以$ f $ -pperiodic点的有限性，相对于固定的非Periodic Point $α$，它们是$ s $ integral。作为一个应用程序，我们在双重索引序列$ \ {f^n（α） - f^m（α）\} _ {n> m \ geq 0} $中获得$ s $单位的界限。如果是一个单一的政治多项式$ f_c（z）= z^2+c $，将$α$固定为关键点0，则对于一个小区域之外的参数$ c $，我们给出了一个明确的界限，这仅取决于$ f_c $的不良减少位置的数量。作为证明的一部分，我们为$ v $ the $ f_c $的$ v $最小的$ f_c $ $ v $ $ k $的$ f_c $的较低限制。
Given a polynomial $f$ defined over a number field $K$, we make effective certain special cases of a conjecture of S. Ih, on the finiteness of $f$-preperiodic points which are $S$-integral with respect to a fixed non-preperiodic point $α$. As an application, we obtain bounds on the number of $S$-units in the doubly indexed sequence $\{ f^n(α) - f^m(α) \}_{n > m \geq 0}$. In the case of a unicritical polynomial $f_c(z)=z^2+c$, with $α$ fixed to be the critical point 0, for parameters $c$ outside a small region, we give an explicit bound which depends only on the number of places of bad reduction for $f_c$. As part of the proof, we obtain novel lower bounds for the $v$-adically smallest preperiodic point of $f_c$ for each place $v$ of $K$.
