Antiholomorphic perturbations of Weierstrass Zeta functions and Green’s function on tori
Antiholomorphic perturbations of Weierstrass Zeta functions and Green’s function on tori
复制标题
Weierstrass Zeta 函数和环面格林函数的反全纯摄动
DOI：
10.1088/1361-6544/aa79cf
复制
发表时间：
2016
期刊：
影响因子：
1.7
通讯作者：
D. Schleicher
中科院分区：
文献类型：
--
作者：
K. Bogdanov;Khudoyor Mamayusupov;S. Mukherjee;D. Schleicher
在Bergweiler和Eremenko（2016年Proc. Am. Math.Soc.1442911 -22），Bergweiler和Eremenko通过研究环面上某族反全纯亚纯函数的动力学，计算了环面上绿色函数的临界点个数。他们还观察到，双曲映射在这个亚纯函数族中以一种相当平凡的方式是稠密的。本文研究了这类亚纯函数的参数空间，它可以表示为Weierstrass Zeta函数的反全纯扰动。一方面，我们给出了一个完整的拓扑描述的双曲分量及其边界，另一方面，我们表明，这些集承认自然参数化相关联的动力学不变量。这解决了Lin and Wang（2010 Ann.Math.172 911-54）中关于上半平面H中绿色函数的临界点数目保持恒定的区域的拓扑的猜想。
In Bergweiler and Eremenko (2016 Proc. Am. Math. Soc. 144 2911–22), Bergweiler and Eremenko computed the number of critical points of the Green’s function on a torus by investigating the dynamics of a certain family of antiholomorphic meromorphic functions on tori. They also observed that hyperbolic maps are dense in this family of meromorphic functions in a rather trivial way. In this paper, we study the parameter space of this family of meromorphic functions, which can be written as antiholomorphic perturbations of Weierstrass Zeta functions. On the one hand, we give a complete topological description of the hyperbolic components and their boundaries, and on the other hand, we show that these sets admit natural parametrizations by associated dynamical invariants. This settles a conjecture, made in Lin and Wang (2010 Ann. Math. 172 911–54), on the topology of the regions in the upper half plane H where the number of critical points of the Green’s function remains constant.
影响因子：
0.9
作者：
S. Mukherjee;S. Nakane;D. Schleicher
通讯作者：
S. Mukherjee;S. Nakane;D. Schleicher
影响因子：
3.1
作者：
H. Inou;S. Mukherjee
通讯作者：
H. Inou;S. Mukherjee