非阿基米德动力学共轭解的发散与收敛
Divergence and convergence of conjugacies in non-Archimedean dynamics
摘要：
我们继续在[21]中研究定义在素特征为p的域上的幂级数f在不同不动点附近的线性化性。自从Herman和Yoccoz [13]在1981年的工作以来，我们知道Siegel的线性化定理[27]对非阿基米德域也是成立的。然而，他们也证明了西格尔定理中的条件“通常”在素特征的域上不满足。事实上，如[21]中所证明的，存在幂级数f使得相关的共轭函数发散。证明了如果一个幂级数f的单项式的次数能被p整除，则f是可解析线性化的.我们发现一个较低的（有时是最好的）边界的大小相应的线性化光盘。在我们发现的线性化光盘的确切大小的情况下，我们表明，使用Weierstrass度的共轭，f有一个中立的周期点的边界上。我们还给出了一类多项式含有一个与p互素的单项式，使得共轭发散。
英文摘要：
We continue the study in [21] of the linearizability near an indif- ferent fixed point of a power series f, defined over a field of prime characteristic p. It is known since the work of Herman and Yoccoz [13] in 1981 that Siegel's linearization theorem [27] is true also for non- Archimedean fields. However, they also showed that the condition in Siegel's theorem is 'usually' not satisfied over fields of prime character- istic. Indeed, as proven in [21], there exist power series f such that the associated conjugacy function diverges. We prove that if the degrees of the monomials of a power series f are divisible by p, then f is analyt- ically linearizable. We find a lower (sometimes the best) bound of the size of the corresponding linearization disc. In the cases where we find the exact size of the linearization disc, we show, using the Weierstrass degree of the conjugacy, that f has an indifferent periodic point on the boundary. We also give a class of polynomials containing a monomial of degree prime to p, such that the conjugacy diverges.
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。
