Newton maps: Fractals from Newton's method for the circle map

被引：0
|
作者：
Cartwright, Julyan H.E. [1 ]
机构：
[1] Inst. Andaluz de Cie. de la Tierra, CSIC-Universidad de Granada, E-18071, Granada, Spain
来源：
Computers and Graphics (Pergamon) | 1999年 / 23卷 / 04期
关键词：
Fractals;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
To understand why two interacting oscillators synchronize with each other, or lock together and resonate at some rational frequency ratio, dynamical-systems theory shows that one should study circle maps and their periodic orbits. One can easily explore the structure of these periodic orbits using Newton maps, derived from Newton's method for finding the roots of an equation. I present here some interesting and beautiful examples of fractals encountered in Newton maps while investigating the periodic orbits of circle maps.
引用
收藏
页码：607 / 612
相关论文
共 50 条
  • [1] Newton maps: fractals from Newton's method for the circle map
    Cartwright, JHE
    COMPUTERS & GRAPHICS-UK, 1999, 23 (04): : 607 - 612
  • [2] Fractals Arising from Newton's Method
    Cilingir, Figen
    FIRST INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2012), 2012, 1470 : 142 - 147
  • [3] NEWTON METHOD, CIRCLE MAPS, AND CHAOTIC MOTION
    SAARI, DG
    URENKO, JB
    AMERICAN MATHEMATICAL MONTHLY, 1984, 91 (01): : 3 - 17
  • [4] THE NEWTON'S METHOD, MATHEMATICA AND FRACTALS: THE HISTORY OF A PAGE
    Rubiano, Gustavo
    BOLETIN DE MATEMATICAS, 2007, 14 (01): : 44 - 63
  • [5] From Newton Fractals to Gradient Fractals in Addition to Zhang Fractals
    Zhang, Yunong
    Qiao, Tianjian
    Liao, Bolin
    Jin, Long
    Chen, Junwei
    2014 IEEE 17TH INTERNATIONAL CONFERENCE ON COMPUTATIONAL SCIENCE AND ENGINEERING (CSE), 2014, : 1237 - 1242
  • [6] On the local classitication of smooth maps induced by Newton's method
    Riaza, R
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2005, 217 (02) : 377 - 392
  • [7] Newton's Fractals on Surfaces via Bicomplex Algebra
    Maggioli, Filippo
    Baieri, Daniele
    Melzi, Simone
    Rodola, Emanuele
    PROCEEDINGS OF SIGGRAPH 2022 POSTERS, SIGGRAPH 2022, 2022,
  • [8] Newton’s method
    Vivek S. Borkar
    Resonance, 2002, 7 (1) : 31 - 36
  • [9] Newton's method
    Meza, Juan C.
    WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL STATISTICS, 2011, 3 (01) : 75 - 78
  • [10] On the Newton method for set-valued maps
    Dias, S.
    Smirnov, G.
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (03) : 1219 - 1230
12345