标题： 牛顿法在奇偶椭圆函数中的动力学 显示英文标题

标题： Dynamics of Newton's method for odd and even elliptic functions

摘要： 我们研究将牛顿法应用于任何奇数或偶数的椭圆函数，其周期格具有任意的周期结构。 对于此类函数，若其极点集与其周期格重合，我们证明其牛顿映射的朱利亚集是连通的，只要不存在赫尔曼环。 此外，我们提供了关于任何奇数或偶数椭圆函数的牛顿法的充分条件，以表现出游荡域与吸引基域共存的现象。 这一现象最初由Florido和Fagella对一类整函数的牛顿法报告过；然而，我们的方法不使用提升技术。 我们还对由$\wp_Λ+b$给出的一个参数族的椭圆函数进行了详细研究，其中$Λ$为任意三角形周期格，$b\in\mathbb{C}$。 我们证明它们相关的牛顿映射不表现出赫尔曼环或贝克域，任何其他肥约组件，包括游荡的，都是有界的。 显示英文摘要

摘要： We investigate Newton's method applied to any odd or any even elliptic function with an arbitrary period lattice. For any function of this type whose set of poles coincides with its period lattice, we show that the Julia set of its Newton map is connected, as long as no Herman rings exist. Moreover, we provide sufficient conditions on the Newton's method of any odd or even elliptic function to exhibit wandering domains coexisting with attracting basins. This phenomenon was first reported by Florido and Fagella for the Newton's method applied to a family of entire functions; however, our approach does not employ the lifting technique. We also provide a detailed study of a one-parameter family of elliptic functions given by $\wp_Λ+b$ with $Λ$ any triangular period lattice and $b\in\mathbb{C}$. We show that their associated Newton maps do not exhibit Herman rings or Baker domains, and any other Fatou component, including wandering, is bounded.