Dynamics of Iterations of the Newton Map of sin(z)

被引：0

作者：

Cloutier, Aimee ^{[1
]}

Dwyer, Jerry ^{[2
]}

Barnard, Roger W. ^{[3
]}

Stone, William D. ^{[4
]}

Williams, G. Brock ^{[3
]}

机构：

[1] Rose Hulman Inst Technol, Dept Mech Engn, Terre Haute, IN 47803 USA

[2] Univ Mississippi, Dept Math, Oxford, MS 38677 USA

[3] Texas Tech Univ, Dept Math & Stat, Lubbock, TX 79409 USA

[4] New Mexico Inst Technol, Dept Math, Socorro, NM 87801 USA

来源：

SYMMETRY-BASEL | 2024年 / 16卷 / 02期

关键词：

complex dynamics; Newton map; trigonometric functions;

D O I：

10.3390/sym16020162

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

The dynamical systems of trigonometric functions are explored, with a focus on s(z)=sin(z) and the fractal image created by iterating the Newton map, F-s(z), of s(z). The basins of attraction created from iterating F-s(z) are analyzed, and some bounds are determined for the primary basins of attraction. We further prove x and y-axis symmetry of the Newton map as well as some interesting results on periodic points on the real axis.

引用

页数：10

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