SPIDERS' WEBS IN THE PUNCTURED PLANE

被引：1
|
作者：
Evdoridou, Vasiliki [1 ]
Marti-Pete, David [2 ]
Sixsmith, David J. [3 ]
机构：
[1] Open Univ, Sch Math & Stat, Milton Keynes MK7 6AA, Bucks, England
[2] Polish Acad Sci, Inst Math, Ul Sniadeckich 8, PL-00656 Warsaw, Poland
[3] Univ Liverpool, Dept Math Sci, Liverpool L69 7ZL, Merseyside, England
来源：
ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA | 2020年 / 45卷
基金：
英国工程与自然科学研究理事会; 日本学术振兴会;
关键词：
Holomorphic dynamics; escaping set; punctured plane; spider's web; TRANSCENDENTAL SELF-MAPS; WANDERING DOMAINS; ESCAPING POINTS; ITERATION; SET;
D O I：
10.5186/aasfm.2020.4528
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Many authors have studied sets, associated with the dynamics of a transcendental entire function, which have the topological property of being a spider's web. In this paper we adapt the definition of a spider's web to the punctured plane. We give several characterisations of this topological structure, and study the connection with the usual spider's web in C. We show that there are many transcendental self-maps of C* for which the Julia set is such a spider's web, and we construct a transcendental self-map of C* for which the escaping set I(f) has this structure and hence is connected. By way of contrast with transcendental entire functions, we conjecture that there is no transcendental self-map of C* for which the fast escaping set A(f) is such a spider's web.
引用
收藏
页码：511 / 531
页数：21
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