Connectivity properties of Julia sets of Weierstrass elliptic functions

Jane Hawkins; Lorelei Koss

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Connectivity properties of Julia sets of Weierstrass elliptic functions

机译：魏斯特拉斯椭圆函数Julia集的连通性

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摘要

We discuss the connectivity properties of Julia sets of Weierstrass elliptic 8 functions, accompanied by examples. We give sufficient conditions under which the Julia set is connected and show that triangular lattices satisfy this condition. We also give conditions under which the Fatou set of 8 contains a toraL band and provide an example of an order two elliptic function on a square lattice whose Julia set is a Cantor set.

机译：我们讨论了Weierstrass椭圆8函数的Julia集的连通性，并附有示例。我们给出了连接Julia集的充分条件，并证明三角形格满足此条件。我们还给出了条件，其中8个的Fatou集包含toraL带，并提供了一个方格上的二阶椭圆函数的示例，其Julia集是Cantor集。

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来源
《Topology and its applications》 |2005年第2期|p.107-137|共31页
作者
Jane Hawkins; Lorelei Koss;
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作者单位

Department of Mathematics, University of North Carolina at Chapel Hill, CB #3250, Chapel Hill, NC 27599-3250, USA;

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原文格式 PDF
正文语种 eng
中图分类高等数学;
关键词
complex dynamics; meromorphic functions; julia sets;

机译：复杂动力学;亚纯函数;朱利亚集;

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专利

1. Ergodic Properties and Julia Sets of Weierstrass Elliptic Functions [J] . Jane Hawkins, Lorelei Koss Monatshefte für Mathematik . 2002,第4期

机译：遍历性质和Weierstrass椭圆函数的Julia集
2. Locally Sierpinski Julia sets of Weierstrass elliptic functions [J] . Hawkins JM, Look DM International journal of bifurcation and chaos in applied sciences and engineering . 2006,第5期

机译：Weierstrass椭圆函数的局部Sierpinski Julia集
3. Graphical exploration of the connectivity sets of alternated Julia sets: M, the set of disconnected alternated Julia sets [J] . Danca M.-F., Bourke P., Romera M. Nonlinear dynamics . 2013,第1a2期

机译：备用Julia集的连通性集的图形浏览：M，断开的交替Julia集的集合
4. On Connectivity Of Julia Sets Of Yang-Lee Zeros [C] . Jian-Yong Qiao, Yu-Hua Li International conference on finite or infinite dimensional complex analysis . 2001

机译：论杨李零的Julia套连通性
5. Dynamical properties of Weierstrass elliptic functions on square lattices. [D] . Clemons, Joshua J. 2010

机译：方格上的Weierstrass椭圆函数的动力学性质。
6. Some new addition formulae for Weierstrass elliptic functions [O] . J. Chris Eilbeck, Matthew England, Yoshihiro Ônishi -1

机译：Weierstrass椭圆函数的一些新加法公式
7. Connectivity properties of Julia sets of Weierstrass elliptic functions [O] . Hawkins Jane, Koss Lorelei 2005

机译：魏斯特拉斯椭圆函数Julia集的连通性

Connectivity properties of Julia sets of Weierstrass elliptic functions

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