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.
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页数：10
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