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

共 50 条

[11] Convergence of asynchronous Jacobi-Newton-iterations
Schrader, U
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 1999, 6 (02) : 157 - 165
[12] Termination of Newton/Chord iterations and the method of lines
Kelley, CT
Miller, CT
Tocci, MD
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1998, 19 (01): : 280 - 290
[13] Convergence of asynchronous Jacobi-Newton-iterations
Schrader, U
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 1996, 76 : 525 - 526
[14] Optimizing ferromagnetic characteristics to reduce Newton iterations
Pahner, U
Belmans, R
Hameyer, K
COMPEL-THE INTERNATIONAL JOURNAL FOR COMPUTATION AND MATHEMATICS IN ELECTRICAL AND ELECTRONIC ENGINEERING, 1999, 18 (04) : 629 - 637
[15] 'No matter when or where or who': Iterations of It's a Sin
Shankar, Louis
JOURNAL OF POPULAR TELEVISION, 2023, 11 (02) : 117 - 133
[16] On the convergence of Newton iterations to non-stationary points
Richard H. Byrd
Marcelo Marazzi
Jorge Nocedal
Mathematical Programming, 2004, 99 : 127 - 148
[17] On the order optimality of the regularization via inexact Newton iterations
Jin, Qinian
NUMERISCHE MATHEMATIK, 2012, 121 (02) : 237 - 260
[18] On the convergence of Newton iterations to non-stationary points
Byrd, RH
Marazzi, M
Nocedal, J
MATHEMATICAL PROGRAMMING, 2004, 99 (01) : 127 - 148
[19] On the number of iterations of Newton's method for complex polynomials
Schleicher, D
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2002, 22 : 935 - 945
[20] On the order optimality of the regularization via inexact Newton iterations
Qinian Jin
Numerische Mathematik, 2012, 121 : 237 - 260

← 1 2 3 4 5 →