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

页码：511 / 531

页数：21

共 50 条

[21] The role of behavior in the evolution of spiders, silks, and webs
Vollrath, Fritz
Selden, Paul
ANNUAL REVIEW OF ECOLOGY EVOLUTION AND SYSTEMATICS, 2007, 38 : 819 - 846
[22] Compositionally Universal Entire Functions on the Plane and the Punctured Plane
Luis Bernal-González
Complex Analysis and Operator Theory, 2013, 7 : 577 - 592
[23] HOW TO COLLECT AND PRESERVE DELICATE WEBS OF SPIDERS
GARDNER, M
SCIENTIFIC AMERICAN, 1963, 208 (02) : 152 - &
[24] Compositionally Universal Entire Functions on the Plane and the Punctured Plane
Bernal-Gonzalez, Luis
COMPLEX ANALYSIS AND OPERATOR THEORY, 2013, 7 (03) : 577 - 592
[25] Webs of theridiid spiders: construction, structure and evolution
Benjamin, SP
Zschokke, S
BIOLOGICAL JOURNAL OF THE LINNEAN SOCIETY, 2003, 78 (03) : 293 - 305
[26] CONCERNING WEBS IN THE PLANE
HAMSTROM, ME
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1952, 58 (06) : 663 - 663
[27] ALTERED GEOMETRY OF WEBS IN SPIDERS WITH REGENERATED LEGS
VOLLRATH, F
NATURE, 1987, 328 (6127) : 247 - 248
[28] Concerning webs in the plane
Moore, RL
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1943, 29 : 389 - 393
[29] Molecular spiders on a plane
Antal, Tibor
Krapivsky, P. L.
PHYSICAL REVIEW E, 2012, 85 (06):
[30] Striking and unusual psychic facts occurred in a series of spiders of the upper diadem, to stretch their webs in the vertical plane.
Roussy, B
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES, 1926, 183 : 374 - 376

← 1 2 3 4 5 →